Combination Merestinib and LY2874455 for Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Participants must have pathologically confirmed relapsed or refractory acute myeloid leukemia (AML) or secondary AML following IWG criteria \[40\]. * For subjects with relapsed AML: evidence of ≥ 5% blasts in the bone marrow or development of extramedullary disease who relapse after: * Allogeneic hematopoietic stem cell transplant, or * A minimum of one cycle of standard cytotoxic chemotherapy or two cycles of any hypomethylating agent-based therapy * For subjects with refractory AML: a minimum of 2 prior induction regimens (example: patients who receive 7+3 followed by 5+2 would count as one induction regimen) or a minimum of two cycles of any hypomethylating agent-based therapy. * For subjects with secondary AML: untreated secondary AML, must have been previously treated for myelodysplastic syndrome (MDS) or myeloproliferative neoplasms (MPN) or MDS/MPN (MDS/MPN) overlap syndrome. * No limit to number of prior therapies. * Patients are considered to have failed available therapies or to be ineligible for or to not be interested in intensive chemotherapies, including allogeneic hematopoietic stem cell transplantation. * Patients with a history of allogeneic stem cell transplantation are eligible for study participation provided the transplant was \> 100 days prior to study enrollment. Patients must not have active graft versus host disease other than grade 1 skin involvement. * Age 18 and older. * ECOG performance status ≤2 (see Appendix A). * Participants must have normal organ and marrow function as defined below: * Direct bilirubin within ≤ 1.5 times the institutional upper limit of normal (ULN). For patients with known Gilbert Syndrome, or if the elevation is believed to be leukemia related, the cut-off of ≤ 3.0 times the institutional ULN is allowable. * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN, unless believed to be leukemia related then ≤ 5 x ULN is allowed. * Serum creatinine ≤ 2.0 x ULN * Females of child bearing potential and males must agree to use barrier method/hormonal methods from start of study until four months after last dose of study drug. Females of child bearing potential must have a negative serum pregnancy test at screening. Females are not considered to be of child bearing potential if they are status post successful surgical sterilization including hysterectomy, bilateral tubal ligation or bilateral oophorectomy, or if they are postmenopausal (absence of menses for 12 consecutive months that is not secondary to prior chemotherapy, anti-estrogens, ovarian suppression or other reversible cause). * The effects of Merestinib and LY2874455 on the developing human fetus are unknown. Small molecular inhibitors of tyrosine kinase receptors are known to be teratogenic. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent document. * Able and willing to undergo the required bone marrow biopsies. Correlative studies are strongly encouraged. Exclusion Criteria: * Participants who have had radiotherapy within 2 weeks, with the exception of localized radiotherapy to palliate extramedullary leukemia where no washout is required. * Participants who have had chemotherapy within 2 weeks or 5 half-lives (whichever is longer) from the last dose of chemotherapy prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier. Hydroxyurea is allowed per treating investigator. IT chemotherapy prophylaxis is permitted. * Participants who are receiving any other investigational agents, with the exception of topical or ophthalmologic therapies for mild graft versus host disease which are permitted. * Participants with known CNS leukemia involvement should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * Individuals with other active malignancies that require concurrent chemotherapy are ineligible. Hormone therapy is allowed. * Subject has a known gastrointestinal disorder that in the opinion of the treating investigator is concerning for malabsorption of oral medications. * Subject is unable to swallow pills. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Patients with current or history of NYHA class III or IV cardiac disease, myocardial infarction with past 6 months, or unstable arrhythmia will be ineligible for study. * Pregnant women are excluded from this study because Merestinib and LY2874455 have the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with Merestinib and LY2874455, breastfeeding should be discontinued if the mother is treated with Merestinib and LY2874455. * HIV-positive participants on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with Merestinib and LY2874455. In addition, these participants are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * Subjects with QTcF interval of ≥ 450 msec if male and ≥ 470 msec if female following or with other factors increase the risk of QT prolongation or arrhythmic events (e.g. heart failure, hypokalemia, family history of long QT interval syndrome) at screening. Subjects with bundle branch block should be reviewed by the Medical Monitor for potential inclusion. * Subjects with known active HBV or HCV (cannot have an elevated viral load of HBV or HCV if known history) are ineligible