This is the best suggestion: just go ahead to Lisbon, give a big 'abraço' to your parents, and get a cheap ticket back to London. By the way, if you eventually plan to go on to Lisbon from London anyway at some point in the not too distant future, you may well be able to get a Lisbon/London/Lisbon round trip cheaper than a London/Lisbon one way. You'll also get more miles, and that's the whole point of FT in the first place.