Following up again:
Per
https://www.aa.com/i18n/travelInform.../scl-club.jsp:
International arriving passengers must have a valid, same-day ticket for departure permitting access through Security.
It sounds like they'd allow access on arrival, regardless of what airline you're connecting to, if you can get to the lounge? LA's connecting flight times are not ideal DFW-SCL-MDZ, so I'm trying to figure out if I can fly another airline SCL-MDZ but get arrivals access with a DFW-SCL boarding pass in J. Obviously I'd prefer the LA lounge, but don't want to push my luck too much.