Medicare drug plans can now cover Eli Lilly & Co.’s obesity drug Zepbound as a treatment for obstructive sleep apnea, news that’s expected to prove a big boost for the drug company.

The biotech plans to start a new trial to confirm the potential for monthly dosing this year. Maintenance doses of Wegovy and Zepbound are given weekly. Metsera links long-acting GLP-1 shot to 7.5 ...