The Rocks stopper, batting at three, crashed four boundaries and a maximum in a 29 minute stint at the crease before he was caught by Benny Howell off the bowling of Ryan Higgins in the ninth over.
Lincoln hit the third-highest total in the Middlesex innings as they posted 148-9 off their allotted 20 overs.
But the 24-year-old could not save stop Gloucestershire scoring 151-8 in 19.2 overs to secure a hard-fought two-wicket win.
The right-handed batsman was a late replacement for South African superstar AB de Villiers. The former Proteas captain withdrew due to a finger injury suffered in both hands.
The goalkeeper has represented both Berkshire and the Middlesex 2nd XI this season and recently bludgeoned 119 off 53 balls in a Second XI T20 game.
Lincoln has been Bognor's undisputed number one since joining from Reading in 2016, but is unlikely to return for the Rocks' 2019/20 BetVictor Premier Division campaign.