I was wondering if there's anyway to make the pipe move up in conjunction to the lift above it.
Yup, and it's even very easy: Instead of just making the platform itself into a lift (((or door, for that matter - and I'm not referring to the fact that you can make complex brush'd doors, what I mean is that you can abuse doors as lifts by setting the "lip" parameter to a high negative value, it's not magic but simple logic))), have the other stuff that you want to be moving, too, selected, too, when you turn the brush(es) into the lift/door.
All brushes that are part of the moving entity will be on the move.