If we are in silly and fairly meaningless speculation mode - and we are here - then I would give a reasonable but not overwhelming chance of BA's return to Lima.

Positive reasons
- Past experience has shown that a BA service does not cannibalise IB's service and prevents leakage to Star / Styteam
- Avoiding transfers even MAD, but particularly USA, has extra advantages to many travellers, particularly older travellers, for which BA can charge
- it's a nice hybrid route, bit of cargo, bit of F&F, plenty of tourism, small bit of business. The lack of business travel therefore won't stop re-instatement
- ideal for 787s and 350s
- seen as a growth area of tourism / nature tourism
- more stable politically than some other parts of South America
- bit of a favourte for staff travel

Negatives
- This is naturally LGW but they just have thirsty 777s
- Peru is not a constituent state in the USA
- Bit expensive to run in terms of crew rest times (but then Cheapo-Crews in LGW mitigates that).
- Route will be more price sensitive than some other places.