Lightning lost by 15 runs as they reached 164-7 in response to their hosts’ 179-6.
Lancashire had slipped to 28-3 in reply before Maxwell and Keaton Jennings shared a century stand.
However, Maxwell was dismissed for 79 late on with Jennings unable to take them across the winning line.
Maxwell said: “Once you lose a wicket it was hard for the next bloke to start.
“You needed time to get yourself in, the spinners were getting a fair bit out of it.
“We were trying to pick our targets and it was going alright, but unfortunately one mistake meant it all unravelled pretty quickly.
“I felt like if I’d batted two more overs, the game would have been pretty much done.
“As it is, one mistake had a ripple effect on the rest.
“The result is probably a bit of a wake-up call for us, we were a bit off in all three departments I thought.
“A bit sloppy with the ball, not our crisp best in the field, we have a lot of improvements to make.
“To still be on top of the table is a good problem to have, but we have some things to work on which we’ll rectify in the next couple of days.
“We’ll look forward to our next games on Wednesday (Northamptonshire Steelbacks) and Friday (Birmingham).”