Safety Study of Subcutaneously-Injected Prandial INSULIN-PH20 NP Compared to Insulin Lispro Injection in Participants With Type 1 Diabetes Mellitus

Inclusion Criteria: * Male or female of age 18 to 65 years, inclusive. Females of child-bearing potential must use a standard and effective means of birth control for the duration of the study. * Participants with Type 1 diabetes mellitus (T1DM) (per World Health Organization \[WHO\] criteria) treated with insulin for ≥24 months. * Participants who use an insulin infusion pump for basal insulin administration must be on the device for at least 90 days prior to screening. * Body mass index (BMI) 18.0 to 35.0 kilograms per square meter (kg/m\^2), inclusive. * Glycosylated hemoglobin A1c (HbA1c) ≤7.5 % based on central laboratory screening results. * Fasting C-peptide \<0.6 nanograms per milliliter (ng/mL). * Participants should be in good general health based on medical history and physical examination and without medical conditions that might prevent the completion of study drug injections and assessments required in this protocol. Exclusion Criteria: * Known or suspected allergy to any component of any of the study drugs in this study. * Previous enrollment in this study. Participants who fail Screening may attempt to rescreen into the study. * A participant who has proliferative retinopathy or maculopathy, and/or severe neuropathy, in particular autonomic neuropathy, as judged by the Investigator. * As judged by the Investigator, clinically significant active disease of the gastrointestinal, cardiovascular (including a history of arrhythmia or conduction delays on electrocardiogram \[ECG\]), hepatic, neurological, renal, genitourinary, or hematological systems. * As judged by the Investigator, uncontrolled hypertension (diastolic blood pressure ≥100 millimeters of mercury \[mmHg\] and/or systolic blood pressure ≥160 mmHg after 5 minutes in the supine position). Three attempts may be performed to measure blood pressure. * History of any illness or disease that in the opinion of the Investigator might confound the results of the study or pose additional risk in administering the study drugs to the participant. * As judged by the Investigator, clinically significant findings in routine laboratory data. * Use of drugs (such as systemic corticosteroids) that may interfere with the interpretation of study results or are known to cause clinically relevant interference with insulin action, glucose utilization, or recovery from hypoglycemia. * Recurrent severe hypoglycemia (more than 2 episodes over the last 6 months) or hypoglycemic unawareness, as judged by the Investigator. * Current addiction to alcohol or substances of abuse, as determined by the Investigator. * Pregnancy, breast-feeding, the intention of becoming pregnant, or not using adequate contraceptive measures (adequate contraceptive measures consist of sterilization, intra-uterine device \[IUD\], oral or injectable contraceptives, or barrier methods). * Mental incapacity, unwillingness, or language barriers precluding adequate understanding or cooperation in this study. * Receipt of any investigational drug within 4 weeks of Screening. * Any condition (intrinsic or extrinsic) that in the judgment of the Investigator will interfere with study participation or evaluation of data. Examples would include: renal insufficiency (serum creatinine \>1.5 milligrams per deciliter \[mg/dL\] for males or \>1.4 mg/dL for females), congestive heart failure required medication treatment, and cardiac disease with New York Heart Association (NYHA) Functional Capacity of III/IV.