I've been looking for a flight LAX-LIM, hoping for the nonstop to be released for a date I can use, but in the meantime I'm finding (through QF searches on Award Nexus) AA LAX-MEX connecting to LATAM MEX-LIM, or a couple weeks ago AA LAX-MIA connecting to LATAM MIA-LIM. (Neither of these worked for me timing wise.)

So there are sometimes connections AA-LATAM that show up in searches through other OW sites. (I haven't researched to see if the individual flights exist as awards, or only the connections.)

(LATAM is the new name for LAN after the merger with TAM.)