I don't know for certain, and it may well depend on whether SFO-LHR is a return leg or an outbound, but in general I would expect SFO-LHR to be much more than SFO-LHR-LIS.

That said, the cost of a walk-up one way is likely to be less than the change fee of sticking the two tickets together.

So I'd self-insure, through-check the bags, and book the trip to LIS as two one-ways so that if I did misconnect and BA didn't look after me (fairly unlikely all in) I'd only have to worry about the outbound.