a lovers cross would be defined as a boyfriend or a girlfriend hanging themselves on an emotional/mental Crucifix for their significant other. Dealing with the pain they're put through for the greater good, thus making themselves a martyr.
'Cause girl you really tried
But for every time that we spent laughin'
There were two times that I cried
And you were tryin' to make me your martyr
And that's the one thing I just couldn't do
'Cause baby, I can't hang upon no lover's cross for you"
Jake: why did you and Mary break up?
Jack: She had me on a lovers cross, and it got unbearable.