A Study of LY2541546 in Women With Low Bone Mineral Density

Inclusion Criteria: * Ambulatory, postmenopausal women, inclusive. * Have low bone mineral density (BMD), defined as a T-score or equivalent BMD absolute value (grams/square centimeter \[g/cm\^2\]) for the lumbar spine of between -3.5 and -2.0, inclusive. * Without language barrier, reliable, and willing to make themselves available for the duration of the study and to follow study procedures. * Willing to take study drug and daily supplements (calcium and Vitamin D). * Normal laboratory tests or laboratory test results determined not clinically significant by the investigator. Serum phosphate and serum calcium must be within normal limits, and platelet level greater than 100,000 cubic millimeters (mm\^3). Exclusion Criteria: * Have received treatment with any of the following medications more recently than 3 months prior to screening Androgen, Calcitonin, Estrogen (including over the counter preparations known to have estrogenic activity), Progestin (including over the counter preparations known to have progestogenic activity), selective estrogen receptor modulators (SERMs) (Raloxifene, Tamoxifen, Toremifene, Clomiphene), or Tibolone. * Have previously used or currently use denosumab, parathyroid hormone (PTH) and/or PTH analogs, strontium ranelate, or parenteral formulations of bisphosphonates. * Have received treatment with any oral bisphosphonate within the last year. * Have received therapeutic doses of systemic corticosteroids for more than one month during the 6 months prior to screening. * Have received therapeutic doses of fluorides (20 milligrams per day) for more than 3 months during the last 3 years, or for more than a total of 2 years, or any within the last 6 months. * Have severe Vitamin D deficiency defined as 25-hydroxyvitamin D less than \<9.2 nanograms per milliliter (ng/mL) \[23 nanomoles per liter (nmol/L)\] at screening. If the serum 25-hydroxy-vitamin D level at screening is less than or equal to 9.2 ng/mL and \<20 ng/mL, participants will receive a loading dose of Vitamin D (at a dose of approximately 100,000 international units (IU) given orally) prior to enrollment. * Have any known bone disorder other than low BMD or osteoporosis. * Have a history of osteoporotic fractures, including known prevalent vertebral fracture or evidence of prevalent vertebral fracture on screening spine X-ray or dual-energy x-ray absorptiometry (DXA), or are considered to be at high risk for fracture. * Presence of any abnormality (such as artifacts or osteophytes) that would confound DXA evaluation of lumbar vertebrae in the L-1 through L-4 region. * Have a history of Bell's palsy, other cranial nerve disorders, or have a history of Temporomandibular Joint and Muscle Disorders (TMJDs). * Have any history of cancer within the previous 5 years, except for excised superficial lesions such as basal cell carcinoma and squamous cell carcinoma of the skin. * Have history or presence of cardiovascular, respiratory, hepatic, renal, gastrointestinal, endocrine, hematological, or neurological disorders capable of constituting a risk when taking the study medication or of interfering with the interpretation of data. * Have acute or chronic liver disease (\[bilirubin \>34 micromoles per liter (µmol/L) or \>2.0 milligrams per deciliter (mg/dL), alanine transaminase \[ALT/SGPT\] \>100 units per liter (U/L), or alkaline phosphatase \>300 U/L)\]. * Have impaired kidney function serum creatinine \>135 µmol/L or \>2.0 mg/dL. * Have known allergy to LY2541546, any of diluents or excipients of LY2541546, or significant allergy to any other monoclonal antibody. * History of excessive consumption of alcohol or abuse of drugs within the last year. * Have poor medical condition or psychiatric risks for treatment with an investigational drug.