A lot of runs and a lot of patience. After buying the lyre, you must interact with it many times. Throughout the process, new dialogue becomes available with Orpheus, who offers tips and tricks. The conversations aren't required to learn the lyre, but they're an excellent addition to the game. In total, it takes 210 interactions with the lyre, consecutively or between every run, before Zagreus finally says he can play the lyre.