Booking these flights for September, any recommendations on sites to use and how far in advance to book these flights? Thank you for your help!
I would book now and try www.skyscanner.com as your search engine.
Use Skyscanner, but from memory, only TAP flies Seville to Lisbon, so prices won't be cheap. The other option is a bus to Faro in Portugal then a train to Lisbon. Easyjet flies Lisbon to Madrid, I believe.
For the best prices and availability, flights should have been booked at the start of the year. European flight prices only head in one direction, so book asap.
In addition to Easy Jet, you might try Vueling, a Spanish low-cost carrier.
I used Kayak for an early morning flight in Sept-believe it or not Iberia was the cheapest-$233 for 2 seats with baggage one way to Lisbon.