Mark debuted for Puerto Rico on June 17, 1983, in a Pan American Games Qualifier vs Surinam at Sixto Escobar Stadium in San Juan.
The first qualification match of World Cup 94 USA was between Dominican Republic and Puerto Rico, played on 21 March 1992, and the Puerto Rican defender Marcos Lugris scored the first goal in qualification.In 1995 Lugris was inducted in the Fordham University Athletic Hall of Fame .
On April 5, 2018, Mark was announced as the Guest Honoree for the 5th Annual FutBoricua.Net Awards Gala in San Juan, Puerto Rico.
At the Gala he was presented with the "Premio Cronica Joe Serralta" for his lifetime achievements with the Puerto Rican National team .In 2020, FutbolBoricua.Net announced its Historic Puerto Rico All Time Best XI Team (El mejor XI en la historia de Puerto Rico), Lugris was named to this team along with his teammates Roberto "Boy" Santana, Wilfredo " Cobre" Vinas and Chris Armas.
On April 17, 2022, the International Federation of Football History and Statistics, named Lugris to its "Mens All Time Puerto Rico Dream Team".