Yes, a Bard can do this
With minor illusion, a Bard can create an auditory illusion for 1 minute, and that illusion can be complex enough to carry out a conversation. There is nothing stopping you from mimicking any kind of sound.
If you create a sound, its volume can range from a whisper to a scream. It can be your voice, someone else’s voice, a lion’s roar, a beating of drums, or any other sound you choose. The sound continues unabated throughout the duration, or you can make discrete sounds at different times before the spell ends.
Of course, since you can copy any sound with a cantrip, it's fair to say the third level spell equivalent, major image, is also capable of doing this. However, note that the visual and auditory components of major image cannot be divorced. You create a visual illusion first, which can produce sounds on its own:
You create the image of an object, a creature, or some other visible phenomenon that is no larger than a 20-foot cube. The image appears at a spot that you can see within range and lasts for the duration. It seems completely real, including sounds, smells, and temperature appropriate to the thing depicted.
Since the illusion has to be visible, you can't make an invisible instrument playing the lute, so for purely auditory illusions, major image is a bit limited.