Linda:

If I understood you correctly, you can list him/her as a co-writer in the copyright application for a lyric or other work.
I'm not sure I would suffer the time and expense involved for a lyric by itself. (It would have to be a "water-walker" of a lyric for me to expend the effort and expense in that direction.)

However, if you are bound and determined to proceed in that direction, without a prior agreement on how the "splits" are apportioned, any Copyright issued will assume 50/50. I believe the copyright apps all require the date of birth of all parties involved. If you don't know his/her d.o.b., then give it your best guess and put a question mark behind the date. That way, at least you gave it your best shot and have attempted to be fair.

All of this presumes that the lyric is really worth going through all the effort and expense involved. I hope you have knowledgeable "ears" available to provide you with good advice about that aspect. Personally, I would wait and copyright formally whenever it becomes a song. (Music and lyrics!)

Legally, I have always read that the lyric is copyrighted the instant you affix the work to paper or recording. Please remember, I'm not a lawyer or barrister and my advice is offerred as nothing more than a personal opinion.

All my best,

Dave Rice