The short answer is "Yes." (Yes!!). Always protect yourself.
The longer/more nuanced answer involves copyright law, which is tricky, court interpretations (trickier-- see the recent "Blurred Lines" verdict), and inter-personal relations (trickiest).
Assuming you are in the US, for the purposes of copyright, both your instrumental track and the version with lyrics are "songs" (even though technically a song is supposed to be sung). When you copyright the version with lyrics, it's not a matter of you owning the underlying musical composition and your artist friend owning the lyrics; the piece becomes one legal asset that is owned by both of you. You both have equal rights to both music and lyric portions, and you both have rights to financial benefits. If this has not already been delineated in a previous agreement, then those rights are split 50-50. It's like you both own a Pontiac; not you own the steering wheel and drive-train and he owns the headlights, tires, and door handles. So you will want to separately file copyright for the track, ideally _before_ you file a copyright for the version with lyrics (and you probably want to file form SR, which can cover the composition and the sound recording, rather than PA which only covers the composition).
If the other copyright has already been filed, here's a very important question or two-- have you seen it (the copyright paperwork)? Is your name on it (with proper credit attribution)? And a follow-up-- Do you have all files and masters related to the project, with some kind of time/date stamp included?
While you two may be getting along now, you never know what the future might hold in terms of conflict, and you should always protect your rights (and resist the temptation to enter into "handshake" deals)...
GJ