You're not looking for HP from weapons, you'll get plenty from Eidolons.

Is anyone in the position where they can't get both...? I mean, you can either farm Ultimate and easily get both, or you can't farm Ultimate and you probably can't get... either?

Hmm. If you can't get both for some reason, it'll depend on how far along do you want to look at. IF you can get Lance to MLB and can store the Silver and Gold drops for the FLB later down the line, then the Lance is the stronger option... in the very, very long run. But, keep in mind that a double-skill will absolutely laugh at single-skill weapons, and there's only one skill in the Lance all the way until FLB. Which is going to be a LONG way ahead for anyone who can't farm Ultimate right now.