Based on my travels to other, non-N. American Hyatts w/lounges (e.g.,
Cairo), I'm learning that some lounges will offer "simple" hot breakfast items in the lounge, if asked. So, on the first morning of my stay, I requested an omelette, and got the cheery response: "And, would you like some sausages with that?"
Alas, it ain't always that easy. I made the same request on Day 2, and got the response, "Sorry, sir, but we don't serve hot items." However, this could be a rookie mistake or training issue, as the same staffer could not process my check-out without assistance.