If we could put one in the orbit of something out around Neptune's orbit, would the distance from Sol be enough that the instruments would not need to be liqued cooled (which supplies is what limits lifespan for JWST)?

It's not the liquid helium that limits JWST's lifespan (as that's in a closed loop), but rather the propellant needed to keep it in a stable orbit. I'm no rocket scientist, but I don't imagine that would be much less of a concern around a further, possibly less stable Lagrange point.