First, not all types of files support metadata, but many do. (mp3 has two types, wav can also have them, probably ogg as well)
Second, not all files of a type will have such data. (wav files in particular usually don't, and i know of players that botch playback if it does contain it... weirdly enough)
But, it's relatively simple to implement a small parser for them.
I'm assuming you will use love.filesystem functions because who doesn't like dragndropping files onto the app, or having every music file in your project's save folder?
You'll need to look up how these tags are stored in the files, search for any headers / magic numbers, and if they exist, read in the data, pretty it up, and that's it.
No concrete examples from me at the moment though.
Also, löve does support tons of other music files besides those 3, but they are the main "culprits".
Doing the same for other filetypes is a similar process, but of course, different. You'd have to implement it differently for all types you want to support this way. Again, not that hard of a task.