A Study of U-500 Insulin (LY041001) in Participants With Type 2 Diabetes

Inclusion Criteria: * Males or females with type 2 diabetes mellitus (T2DM) * Are current users of U-100, U-200 and/or U-300 insulin/analog as, basal, premixed and/or basal/bolus delivered with any injection device (pens and/or syringe/vial but excluding continuous subcutaneous infusion (CSII)/insulin pump use in the preceding 3 months), taking a total daily dose (TDD) of greater than or equal to (≥) 150 units (U) or at least one dose greater than (\>) 100 U as part of a multiple daily injection (MDI) regimen and TDD less than or equal to (≤)3.0 units per kilogram (U/kg) * Concomitant antihyperglycemic agent(s) (AHA) therapy may include: metformin (MET), dipeptidyl peptidase 4 inhibitors, pioglitazone (doses ≤30 milligrams per day (mg/day)), glucagon like peptide (GLP)-1 receptor agonists, sodium-glucose co-transporter-2 (SGLT2) inhibitors, except in combination with GLP-1 receptor agonists * Participant's antihyperglycemic agent (AHA) therapy must have been stable for ≥3 months (except for weekly GLP-1 receptor agonists which must have been stable for ≥4 months) * Have hemoglobin A1c (HbA1c) 7.5-11.5 percent (%) Exclusion Criteria: * Have type 1 diabetes mellitus (T1DM), or other types of diabetes mellitus apart from T2DM * Have known hypersensitivities or allergies to insulin, excipients contained in insulin products, or related compounds * Have used U-500R within 3 months prior to screening * Have used rosiglitazone, pramlintide, once weekly or twice daily exenatide, or other injectable or oral antihyperglycemic agent(s) not listed in the inclusion criterion; or are taking oral antidiabetic medications at doses exceeding the respective product labels * Have had a blood transfusion or severe blood loss within 3 months prior to screening or have known hemoglobinopathy, hemolytic anemia, or sickle cell anemia which may affect reliability of HbA1c measurements