In my experience, I'd say you're out of luck. After you pass through Immigration and Customs, you don't have access to any lounges I know of, and as the LATAM lounge apparently closes at midnight, it'd be a moot point by the time you exit Immigration and Customs.

For the next day: when connecting from international to domestic flights, after flying biz class on AA, United or Delta, we've ended up using the cramped and basic American Express Centurion Club, since it's outside security. As far as I know, no airlines (TAM, Gol, Avianca, Azul) have lounges for domestic flights, but I could be wrong.

We were going to use the new Star Alliance Lounge in Terminal 3 when we transited outbound recently, but had to rush to get from Terminal 1 (Gol) to T3 (United) that we did not have time to go to the lounge.