Do a Google Flights search for your dates from LAX to LIS and you can see the prices and routes flown. You have to do at least 2 segments, but you have plenty of choices between BA, AF, LH, AA/US, UA, and DL (depending on whether you prefer to do 1 long flight LAX-Europe and then short hop to LIS or a cross-country flight to an East Coast gateway city and the trans-Atlantic hop to LIS). You can also look at routehappy.com to get some sense of which economy seats are more comfortable.