One of the summer fares available from New York JFK is Lisbon via Delta nonstop flights. Ticket prices in July and August are down to $497 on KLM and Air France websites for codeshare flights on Delta-operated nonstop aircraft.
KLM codeshare ticket for Delta operated nonstop flights.
New York JFK – Lisbon, Portugal LIS – New York JFK nonstop
You can be really adventurous and cut the fare to $402 round trip flying Royal Air Maroc Airlines in June on a 787 Dreamliner aircraft with overnight transit layover in Casablanca CMN, Morocco outbound, inbound or both ways.
Royal Air Maroc New York JFK – Casablanca CMN – Lisbon LIS – Casablanca (20 hour overnight layover) – New York JFK