I did this exact same trip some 14 months ago, though on one ticket BA to Latam. No immigration. I cannot remember which Lounge I used, but I do remember being a tad bored since the BA flight arrived early and there was not a lot to do, apart from a shower and copious coffees to stay awake. IIRC I had 6 hours between flights. For 9 hours a hotel (even if you have to go landside) could be a good decision.