AA 361 then LA 2991 at Miami
Austin → Miami → Lima
Timetable, Miami time
16:48AA 361 from Austin at the gate
16:45LA 2991 to Lima leaves the gate
23 h 57 apart on the timetable, overnight
LA 2991 leaves 23 h 57 after AA 361 arrives on the timetable: more than half a day, so not a connection we count.