Pembrolizumab + Imprime PGG for Metastatic Non-small Cell Lung Cancer After Progression on First-Line Therapy: Big Ten Cancer Research Consortium BTCRC-LUN15-017

Inclusion Criteria: * Male or female ≥ 18 years of age at time of consent. * Subjects with histologically or cytologically confirmed non-small cell lung cancer (NCSLC). * Subjects with stage IV non-small cell lung cancer as defined by American Joint Committee on Cancer (AJCC). * Phase Ib: Subjects who progressed after first-line platinum-based chemotherapy and who are candidates for second-line therapy. * Phase II: Subjects who have progressed on first-line systemic therapy (either platinum-based chemotherapy with or without immune checkpoint inhibitor or immune checkpoint inhibitor as first line therapy) who are candidates for second-line systemic therapy. Patients with early stage cancer will also be eligible if progression occurs: * within 6 months of adjuvant chemotherapy after curative resection * within 6 months of adjuvant chemotherapy after curative resection while on adjuvant immunotherapy, currently only available as part of a clinical trial * within 6 months of curative surgery if chemotherapy is given in the neoadjuvant setting * within 6 months of completion of chemoradiation (or 6 months from completion of consolidation chemotherapy if administered after concurrent chemoradiation) * within 6 months of completion of chemoradiation or consolidation chemotherapy (if administered) while on consolidation immunotherapy, a setting for which durvalumab is FDA approved. * Phase II: Subjects with an EGFR or ALK mutation who are no longer candidates for TKI therapy and have progressed on standard systemic therapy (either platinum-based chemotherapy with or without immune checkpoint inhibitor or immune checkpoint inhibitor as first line therapy). * Phase II only: Measurable disease according to RECIST v1.1 (Section 8) obtained by imaging within 28 days prior to study registration. Phase Ib: subjects may enroll with or without measurable disease. * Phase II only: Subjects must have presence of peripheral blood levels of IgG anti-β-glucan antibody (ABA) of ≥ 20 μg/mL as determined by an ELISA test within 90 days prior to study registration. * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 within 28 days prior to study registration. * Life expectancy of 6 months or greater as determined by the treating physician. * Adequate hepatic function within 28 days prior to study registration defined as meeting all of the following criteria: * total bilirubin ≤ 1.5 × upper limit of normal (ULN) OR direct bilirubin ≤ ULN for subjects with total bilirubin levels \> 1.5 x ULN (except subject with Gilbert's Syndrome, who can have total bilirubin \< 3.0 mg/dl) * aspartate aminotransferase (AST) ≤ 2.5 × ULN or ≤ 5 × ULN for subjects with known hepatic metastases * alanine aminotransferase (ALT) ≤ 2.5 × ULN or ≤ 5 × ULN for subjects with known hepatic metastases * Adequate renal function within 28 days prior to study registration defined by either of the following criteria: * Serum creatinine ≤ 3 mg/dL * if serum creatinine \> 3mg/dL, estimated glomerular filtration rate (GFR) ≥ 20 mL/min * Adequate hematologic function within 28 days prior to study registration defined as meeting all of the following criteria: * hemoglobin ≥ 9 g/dL; subjects requiring transfusion will be eligible to start study * and absolute neutrophil count (ANC) ≥ 1.5 × 109/L * and platelet count ≥ 100 × 109/L * Adequate coagulation functioning within 28 days prior to study registration defined by either of the following criteria: * INR \< 1.5 × ULN * for subjects receiving anticoagulant, the subjects must, in the investigator's opinion, be clinically stable with no evidence of active bleeding while receiving anticoagulant therapy. The INR for subjects on warfarin should be in the therapeutic range. Low molecular weight heparin (LMWH) is allowed. * Provided written informed consent and HIPAA authorization for release of personal health information, approved by an Institutional Review Board (IRB). NOTE: HIPAA authorization may be included in the informed consent or obtained separately. * Women of childbearing potential (WOCP) must not be pregnant or breast-feeding. A negative serum or urine pregnancy test is required within 72 hours of study registration. If the urine test cannot be confirmed as negative, a serum pregnancy test will be required. * Women of childbearing potential (WOCP) must be willing to use two effective methods of birth control such as an oral, implantable, injectable, or transdermal hormonal contraceptive, an intrauterine device (IUD), use of a double barrier method (condoms, sponge, diaphragm, or vaginal ring with spermicidal jellies or cream), or total abstinence for the course of the study until 120 days after the last dose of study drug. NOTE: Women are considered to be of childbearing potential unless they are postmenopausal (≥45 years of age and has not had menses for greater than 12 consecutive months), surgically sterile (bilateral tubal ligation, bilateral oophorectomy, or hysterectomy) or not heterosexually active for the duration of the study and at least 120 days after the last dose of study drug. * Men who are not surgically sterile (vasectomy) must agree to use an acceptable method of contraception. Male subjects with female sexual partners who are pregnant, possibly pregnant, or who could become pregnant during the study must agree to use condoms from the first dose of study drug through at least 120 days after the last dose of study drug. Total abstinence for the same study period is an acceptable alternative. * Willingness and ability to comply with scheduled visits (including geographical distance), treatment plans, laboratory tests, and other study procedures. Exclusion Criteria: * Surgery within 4 weeks prior to study registration except for minor procedures. NOTE: Hepatic biliary stent placement, PleurX catheter, port replacement, ureteral stent or other minor surgeries are allowed. NOTE: Subject must have adequately recovered from the toxicity and/or complications of major surgery prior to study registration, as determined by the treating physician. * Patients with known untreated or active central nervous system (CNS) metastases. Subjects suspected to have brain mets should undergo brain MRI (or CT head if MRI is not feasible) to exclude brain metastases. Patients with treated brain metastases will be eligible as long as their symptoms are improving or achieved new baseline and not requiring steroids for at least 2 weeks. Patients with leptomeningeal disease will be excluded regardless of clinical stability. * Previously received a solid organ transplant or allogeneic progenitor/stem cell transplant. * Received a live vaccine within 30 days prior to the first dose of trial treatment. Examples of live vaccines include, but are not limited to: measles, mumps, rubella, chicken pox, yellow fever, rabies, BCG, and typhoid (oral) vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g. Flu-Mist®) are live attenuated vaccines and are not allowed. * History of blood clots, pulmonary embolism, or deep vein thrombosis unless on adequate anticoagulant therapy as determined by the treating investigator (subject must be on stable dose for 2 weeks) and all symptoms have resolved. * Known history of human immunodeficiency virus \[(HIV) HIV 1/2 antibodies\]. * Known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Current use of immunosuppressive medication at time of study entry. The following are exceptions to this exclusion criterion: intranasal, inhaled, topical steroids, or local steroid injections (eg, intra-articular injection); steroids as premedication for hypersensitivity reactions (eg, CT scan premedication). Cases requiring systemic corticosteroids at physiologic doses must be discussed with Big Ten CRC and HiberCell prior to enrollment. * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent. Exceptions include: patients with controlled diabetes type 1, controlled hypo- or hyperthyroidism, resolved childhood asthma/atopy, vitiligo, or psoriasis not requiring immunosuppressive treatment. * Received prior chemotherapy, an immune checkpoint inhibitor, or radiation therapy within 2 weeks prior to study registration or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events from previously administered agents. NOTE: Subjects with alopecia, grade ≤ 2 sensory neuropathy or other grade ≤ 2 AEs not constituting a safety risk based on investigator judgement are an exception to this criterion and can still be considered for the study. * Any clinically significant infection requiring anti-infective treatment. Patients with infection that is adequately treated will be eligible. * History of interstitial lung disease requiring immunosuppressive/steroids or history of immunotherapy related pneumonitis that has required steroids or immunosuppression in the past. * Known history of active tuberculosis. * Any other severe, uncontrolled medical condition, including uncontrolled diabetes mellitus (defined as a Hemoglobin A1C ≥ 9% in subjects with a prior history of diabetes, 28 days prior to study registration) or unstable congestive heart failure (Stage III-IV of the New York Heart Association Functional Classification). * Previous known allergy or intolerance to pembrolizumab or any of its excipients. * Previous exposure or known allergy to Imprime PGG or any of its excipients. * Known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies. * Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or investigational product administration, interfere with protocol compliance, or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the subject inappropriate for enrollment in this study. * Presence of any non-healing wound, fracture, or ulcer within 28 days prior to study registration. * Any mental or medical condition that prevents the subject from giving informed consent or participating in the trial. * No prior malignancy is allowed except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, in situ breast cancer, Gleason ≤ grade 7 prostate cancers, low grade papillary urothelial carcinoma or other cancer for which the subject has been disease-free for at least 2 years. And no additional therapy other than hormonal therapy is required for anticipated to be required during the trial period. * Treatment with any therapeutic investigational agent within 28 days prior to study registration.