I'm looking at picking up a Fender P bass with a split Lollar

I play a G&L LB100 with a Lollar.
So basically exactly what you're looking for.
They sound great! It's an excellent pickup. a slightly more modern sound.
Great low end and mid forward, nice clean highs. I love mine!
you can hear it hear if you like - in a full band setting. I play with a pick and pretty aggressively.
these 2 songs are through an old Peavey PA head with some overdrive from a Catalinbread SFT pedal:


This album is mostly through an old Bassman head and I can't remember what kind of cab:

 

Which model P Bass? Fender puts different pickups in different models.

 

I’m not positive, but I think that bass came with a Custom Shop ‘60s pickup. IMO, the CS ‘60s is a pretty decent pickup. I would consider the Lollar an upgrade, but for live music I don’t know if I would bother making the change. If the bass already has the Lollar installed, it should sound really good.