I believe that brunch at Palo is from 10:30 to 1:00 on sea days. I understand that they also offer it on Key West day on the western itinerary, but it ends earlier.
I had Eggs Benedict at Palo at the brunch, and I think I also had them once at Lumière's. I'm pretty sure about this, but not positive. I haven't eaten breakfast at Lumière's since fall of 2000. On recent cruises, we've done breakfast at Topsiders. We like the omelets made to order and eating outside on the back of deck 9.