I would go further and edit (this is just me playing. when i go and edit something it's about me putting it in my personal style, I'm not saying I think it would necessarily be better this way - just wanted to see how I'd warp this to my own voice) to this:
It is NOT the same as what you posted though. A relationship locks
eyes across a crowded room.
Some beautiful someone,
the rest of your lives
imagined for the rest
of the day.
That's interesting. This construction forces "your" to refer to "A relationship" and "Some beautiful someone", eradicating the implicit "I" of the poem. Also, there is no real "who" to whom the eyes in "eyes across a crowded room" belong to, which forces it to also be a verb in the context of the singular line. See? Line breaks are wicked important!