Skyscanner website will tell you the cheapest day to fly. Don't try to buy off that website though, just find out what airline is cheapest and go direct to their website. Norwegian do a return for around the price you quote JFK to Lisbon with 1 change in Copenhagen, depending on your dates. That's the cheapest quote that Skyscanner gives me. If you're willing to make more than 1 change it gets cheaper but probably not cheap enough for the added time and hassle.
This price seems about correct to fly at just about the most expensive and popular time of the year to travel to Europe.
TAP Portugal fly non stop EWR - LIS.
If you going from June to August from the States to Europe you aren't going to get a deal. Best thing to do is to book multiple destinations to make the trip more worth it.
-:- Message from TripAdvisor staff -:-
This topic has been closed to new posts due to inactivity. We hope you'll join the conversation by posting to an open topic or starting a new one.
To review the TripAdvisor Forums Posting Guidelines, please follow this link: http://www.tripadvisor.com/pages/forums_posting_guidelines.html
We remove posts that do not follow our posting guidelines, and we reserve the right to remove any post for any reason.