LSU (7-0) is off to its best start in five seasons -- when it won its first eight games.
Thornton, who played just 20 minutes, also tied his career-high with five assists and made 6 of his 9 field goal attempts.
Martin, who played only 17 minutes, came off the bench and shot 6-for-7 from the field, making a season-best four 3-pointers.
Ibrahim Kpaka led Grambling (2-6) with 14 points. Jarred Riley contributed 10 points. Andrew Prestley, Grambling's top scorer this season, scored seven points -- nearly six less than his per-game average.