$686 - Flights to Lisbon Portugal from San Francisco
Try searching for flights on Tuesday through Thursday.
If you give yourself a few weeks, I haven’t seen flight prices go higher than $706.
If you are forces to take a long layover in Heathrow, be advised that you can leave the airport, and check out London for a few hours, but if you do so, be advised that security lines to get back into the airport can be quite difficult.
More information on leaving London, Heathrow Airport here
Total flight time to Lisbon from San Francisco is anywhere form 16 to 20-something hours including the layover stop.