Grishka, yes "De t'aver vist bèu chivalièr me costarà la vida" (this is how we'd spell it now) does mean what you say, it will cost her life.
My feeling is that either
- the verse is actually supposed to be intended for the audience and I see it as meaning he will kill her whatever the reason, probably because she should have stayed in the leper hospital (maybe "hospital" isn't exactly accurate!) instead of wandering about. I doubt that it could be because she could report him as behaving badly -maybe "to help to cross the wood" would be considered at that time on the same way as some drivers consider taking a female hitch-hiker in their car- but it could also be out of frustration because he couldn't "help her to cross the wood".
- or the verse is intended for the knight in the logic of her story, i.e. when she's back to the leper hospital they'll kill her for enfringing the rule, so he can leave her alone and let her go.
I don't think that it's one of those songs in which the young lady kills herself to avoid sex.