Lamptey was a constant menace in first half and created opportunities for Jakub Moder and Neal Maupay, while Leo Trossard also cracked the woodwork.
Moder and Maupay also missed further chances after the break and substitute Solly March also had two efforts well-saved by Leeds stopper Meslier.
Albion had 20 attempts in total but in the end they were thankful for two sharp saves from returning goalkeeper Rob Sanchez who denied Tyler Roberts.
The point moves Brighton up to eighth in the table while Leeds remain in 17th.
Scroll down and click through to see who shone and who struggled for Albion.
9. Pascal Gross 6/10
Gross covered so much ground in the midfield and a danger from set-pieces.
10. Leo Trossard 8/10
Deeper role with Maupay back in the team. Cracked the woodwork with a fine first half effort. A real threat and on top of his game
11. Neal Maupay 5/10
Missed an early chance when his left footed effort from close range ballooned over. Another bad miss when his right foot from Lamptey's cross went wide. Looked fuming when he was subbed for Locadia
12. Solly MArch 7/10
On for Lamptey and had one stinging effort deflected just over and another effort well saved by the Leeds stopper. Made an impact.