The two teams could not be separated in 90 minutes of football, but Lille recorded a 5-3 victory in the shootout.
The Toffees will now face Porto on Sunday night in the same competition, before their pre-season finishes with friendlies against Blackburn Rovers and Valencia ahead of their Premier League opener against Wolverhampton Wanderers on August 11.
Everton had the ball in the back of the Lille net in the 25th minute when Davy Klaassen turned home, but the offside flag cut the English club's celebrations short.
Lille's best chance of the first period arrived in the 35th minute when Thiago Mendes found space in the final third before striking towards goal, and his effort rattled against the crossbar.
Anwar El-Ghazi struck a free kick into the Everton wall early in the second half as the score remained level, and it was the French side that continued to create the better chances in the Algarve Football Cup.
EVERTON: Stekelenburg; Robinson, Williams (Holgate 84'), Pennington, Kenny; Connolly (Davies 79'), Besic, Klaassen (Dowell 79'), Vlasic; Ramirez (Mirallas 46'), Niasse
LILLE: Maignan; Ikone (Benzia 65'), Celik (Malcuit 86'), Droehnle (Alonso 76'), Edgar Le; El Ghazi, Faraj (Bamba 65'), Gabriel, Mendes (Xeka 65'); Mothiba (Pepe 76'), Zekaj (Maia 76')