[Bungleau]

Which gate? The wing gate in the middle of the front entrance room?

If that's the case, head up like you're going to see the lich, but turn right to stabilize the walkway. Then walk over the walkway to that main entrance room, and head to the entrance elevator.

Failing that, you can go back into the pool, picking any of the tunnels that you've already cleared. You should run into minimal additional company, and all the tunnels deposit you back in the main entrance area again, IIRC.