You are probably going to have to wait until you get to Lima for a seat assignment. LATAM has a longstanding practice of not assigning seats in advance for passengers traveling on codeshares, regardless of status. I recently traveled on Delta/LATAM (Codeshare) BOS-MIA-LIM and when checking in with Delta in Boston, they could not even issue a boarding pass for the MIA-LIM flight. Instead, on arriving in MIA I had to leave the terminal, check in with the LATAM counter, get the boarding pass and seat assignment, and then go back through security to the gate.