More often than not my LRs encounters with the Navy or Police end without PvP. But if I didn't run away, then you can't possibly expect the RP not to end in PvP. The fact is when opposing roles meet, they're not just going to let their foes walk away.
I can't expect any RP I have with a Vigilantee on my LR to end in anything less than PvP, because that would be against what vigilantees are about. The more interesting RP involves two roles who are not opposing forces meet.
There are many RP opportunities with people who are not your enemies also. So if you're sick of your RP always ending in PvP, try roleplaying more ofte with your allies or people who you are not enemies with. Because if you go seeking RP from your enemies, then you are also inadvertantly seeking PvP. Which, believe it or not, is also a part of your RP interaction with them.
Of course, the most satisfying RP to me are ones that could have ended in PvP but didn't.