A Study of Dulaglutide (LY2189265) in Participants With Type 2 Diabetes Mellitus

Inclusion Criteria: * Have type 2 diabetes mellitus (based on the World Health Organization's \[WHO\] diagnostic criteria) * Have been treated with an SGLT2 inhibitor, with or without metformin, for at least 3 months prior to study entry (minimum required doses for that period for allowed SGLT2 inhibitors: empagliflozin 10 mg, dapagliflozin 5 or 10 mg \[per country-specific label\], canagliflozin 100 mg); minimum required dose for metformin, if used, is ≥1500 mg/day and must be reached (or highest tolerated dose which is acceptable with documented gastrointestinal \[GI\] intolerability) * Daily doses of all allowed oral antihyperglycemia agent (OAMs) must have been stable for at least 12 weeks (±3 days) prior to randomization (study enrollment); daily doses of SGLT2 inhibitor and metformin, if used, will be considered stable during this period if: * all prescribed daily doses were in the range between the minimum required dose and maximum-approved dose per country-specific label; and * \>90% of prescribed daily doses were equal to the dose at randomization * Have HbA1c ≥7.0% and ≤9.5% at study entry and approximately 1 week prior to randomization * Have body mass index (BMI) ≤45 kilograms per meter squared (kg/m\^2) and agree to not initiate a diet and/or exercise program during the study with the intent of reducing body weight other than the lifestyle and dietary measures for diabetes treatment Exclusion Criteria: * Have type 1 diabetes mellitus * Have been treated with any other OAMs (other than SGLT2 inhibitors and metformin), glucagon-like peptide-1 receptor agonist (GLP-1 RA), pramlintide or insulin 3 months prior to study entry, or between study entry and randomization; or initiate metformin between study entry and randomization; short-term use of insulin for acute care (≤14 days) during the 3-month period prior to entry is not exclusionary * Have any condition that is a contraindication for use of the GLP-1 RA class or the SGLT2 inhibitor class (per country-specific labels) at study entry or develop such condition between study entry and randomization * Have acute or chronic hepatitis, signs and symptoms of any other liver disease other than nonalcoholic fatty liver disease (NAFLD), or alanine transaminase (ALT) level \>2.5 times the upper limit of the reference range, as determined by the central laboratory at study entry; participants with NAFLD are eligible for participation in this trial * Had chronic or acute pancreatitis any time prior to study entry * Estimated glomerular filtration rate (eGFR) \<45 milliliters(mL)/minute/1.73m\^2, calculated by the Chronic Kidney Disease-Epidemiology (CKD-EPI) equation, as determined by the central laboratory at study entry and confirmed at lead in * Have any self or family history of type 2A or type 2B multiple endocrine neoplasia (MEN 2A or 2B) in the absence of known C-cell hyperplasia (this exclusion includes participants with a family history of MEN 2A or 2B, whose family history for the syndrome is rearranged during transfect \[RET\]-negative; the only exception for this exclusion will be for participants whose family members with MEN 2A or 2B have a known RET mutation and the potential participant for the study is negative for the RET mutation) * Have any self or family history of medullary C-cell hyperplasia, focal hyperplasia, carcinoma (including sporadic, familial, or part of MEN 2A or 2B syndrome) * Have a serum calcitonin ≥20 picograms/mL as determined by the central laboratory at study entry