To deliver a performance of rhyming poetry or rap lyrics that one has written or thought up. A possessive pronoun can be used between "run" and "rhymes" The kids runs rhymes like a professional. I'd be shocked if we didn't see a rap album out of him in the next couple of years. She had been running her rhymes at a number of amateur poetry events before she finally got he nerve to submit her work to a publisher.
run one's rhymes
Sl. to say what you have to say; to give one's speech or make one's plea. Go run your rhymes with somebody else! I told him to run his rhymes elsewhere.
run one’s rhymes
tv. to say what you have to say; to give one’s speech or make one’s plea. (Collegiate.) Go run your rhymes with somebody else!