Lawler made 119 in 124 balls - including three sixes - after coming in at number four with his side 28/2 as the MCC Schools outfit posted a competitve 262/7 in their 50 overs.
The Monmouth School pupil, who was skippering MCC Schools, put on 148 for the third wicket with Jack Mynott (55) of Dauntsey’s School. Opening bowler Saqib Mahmood was the pick of the bowlers for ESCA, taking 2/39 in a spell of nine overs.
ESCA's response started poorly, with the loss of Jay Weatherley in the third over, but the match defining partnership (also of 148) for the second wicket between Harry Dearden and Haseeb Hameed put their side right on top.
There was heartache for the otherwise excellent Dearden when within just six runs of a ton though, as a mix-up with Hameed led to him being run out by a direct hit at the non-striker's end.
ESCA wobbled briefly, with Hameed dismissed for 70 and Anuerin Donald for a first ball duck - both wickets falling to brilliantly named off-spinner Henry Blofield.
But the next pair of Mosun Hussain (41*) and captain Rob Jones (45*) first steadied the ship, before accelerating to victory in the 46th over.
This was the sixth year that the ESCA team, made up of the pick of players from the previous year's Bunbury Festival, and the MCC Schools side, comprised of the pick of the players to have played in schools cricket against MCC, have met one another at Lord's.
Bunbury CC founder David English spoke to Lord's TV during the match about the fixture and the importance of the game in schools to the development of the senior England team. The vast majority of the current England side competed in the Bunbury Festival as schoolboys.