Fragata was the more lively place on Sunday, but Lagoa was still pretty good. Sundays started about the same time as any other day, ~3:30-4, but maybe with more garotos showing up early.
To extract maximum Brazil goodness time, I usually booked the latest red-eye flight home. For an economical airport transfer, I would go to Tiete bus station in the morning, leave my luggage at the deposit on the ground floor (around $5), then buy the airport express bus ticket for that night. From either Lagoa or Fragata, it's a 20-30 minute subway ride to Tiete. A taxi directly from the sauna to the airport would be more convenient, and more costly, but I'm not sure how much faster it would be since the taxi would have to wade through miles of central SP surface traffic.