I dropped my daughter off at LAX three weeks ago on the Saturday after Thanksgiving. The airport was extremely busy; her flight was full. It wasn't as crazy as the Sunday or Monday that immediately followed, but I'd definitely prefer avoiding a connection from an international to domestic flight at any US airport on Thanksgiving weekend; first, in case that your flight from Europe to the US is late due to weather or mechanical delays, it would be extremely hard to get a party of four rebooked on later flight; second, even if you don't experience delays, you are likely to encounter extremely long lines at TSA security checkpoints after clearing US immigration and customs at your port of entry to the US.

If I were in your position, I'd connect at MAD or CDG rather than at LHR. Arriving from LIS at MAD or CDG, you will not have to go through security there before boarding a flight to the US. At LHR, in addition to the hassle of switching terminals, you will have to go through security. I had the misfortune of connecting at LHR twice this year en route from Europe to the US; in August, it took 45 minutes and I got to the gate long after boarding had already started, more recently in November, it took 40 minutes. The bus ride from T5 to T3, the last time that I had such a connection approx 10 years ago, took almost half an hour.