It's a long way off yet - they need to merge their booking systems first & there's been no news on that yet. Their last attempted systems merger was a disaster - the websites! Even today, a PNR issued by Latam Brasil isn't recognised by the rest of Latam(& vica versa). Using Latam Brasil's website often lands you on tam.com.br pages & Latam's other websites often land you on lan.com sites. Th Tam cargo's website now goes to an ABSA Cargo website(the name they had BEFORE they became Tam Cargo!).

So they haven't managed yet to merge their booking systems, crew, websites or frequent flyer programs. I think getting JJ flight codes onto LA is a LONG way down the list!