If you can 'rap' your lyrics then they can be sung. It's a question of meter, rhythm, and (normally) rhyme - in other words: prosody.
Although I'm still a hobby lyricist after more then ten years of lyrics writing I have developed some kind of market by writing to match other people's music. I'm writing for three bands and several individual artists at the moment (mind, there is no big money involved, just some recognition). There are only few writers who offer this - AND YOU DON'T HAVE TO DO ANY MUSIC YOURSELF ;-)
I must admit, that I do play the guitar, and I sing, and I write songs for my own pleasure. But then, I'm a very lousy musician, so my musical skills definitely would NOT make me a good lyricist.
If you can write poems that flow well, you can also write lyrics that flow well. You only need to observe their different structures, mainly the chorus - the outstanding repeated part of lyrics.
Look out for partners to write the music to match your words or, even better, whose tunes you can write matching lyrics for. There are much too many lyrics writers who simply hope that their lyrics will be 'discovered' some day. Most likely, that won't happen.
Have fun,
Bernd