In Development

It has been said already that though Unicorns know magic, they only have a little bit specific to their cutie mark, the rest are simple things like picking stuff up. (For example Rarity has her unique spell of finding gems) So Lyras magic would most likely be specific to actually strumming the instrument.
Only Twilight (and Trixie (who has their special talent being magic itself)) can cast lots of variable spells.

I thought it was just most unicorns don't need a wide variety of magic so they don't learn more than a couple of spells.

As said by Spike and Twilight in episode 6 of season 1 (Right after the intro song) They both say that Unicorns only have a little magic to help them with their special talent. Unless their talent is magic.

I interpreted that part differently, as if it was just a "i don't have time to learn a huge number of spells" sort of thing rather than "I am incapable of learning more than a couple of spells" thing.

I might be over thinking this, but it sounds like a justification for ensuring balance among different species in a MMORPG. Which i would totally pay for.