Possible suggestion: Anyone ever talked the Olive 8 into allowing them to walk across the street from the Grand (suitably dressed, especially out of respect for the size of the favor) and use their pool? Say, ask the Grand Lounge or lobby concierge, or the front desk manager to intercede -- if not asking the staff at the Olive 8 directly? I would try.

Another pool that might serve, though not a lap pool per se, is the indoor one at the Chesapeake resort. It's possible that you'd only encounter other lap swimmers first thing in the morning -- though I can't personally vouch for that... And the room the pool's in sometimes seems to be a "steam room" itself. Don't remember if there is an actual steam room. Wish I could think of another "urban" one. I can't think past the PH Buenos Aires, which obviously doesn't meet a key criterion. But it might add to the discussion for others looking to this thread, but without that constraint.