Marsh was especially harsh on GT spinner Rashid Khan in the 12th over, milking him for 25 runs, including two sixes and three boundaries, as the Australian reached the 100-run mark off 56 balls.
Earlier, Marsh also shared a 91-run opening-wicket stand with Aiden Markram (36).
GT have already secured a playoff berth, while LSG have been eliminated from the playoff race.
Brief scores: Lucknow Super Giants: 235 for 2 in 20 overs (Aiden Markram 36, Mitchell Marsh 117, Nicholas Pooran 56 not out; Sai Kishore 1/34). PTI AM AM SSC SSC