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.
1. Robert Sanchez 7/10
Didn't have too much to do but what he did, he did well. Great save with his feet to deny Roberts on 82 and then from the resultant corner. Good distribution.
2. Joel veltman 6/10
Veltman Given the nod ahead of Shane Duffy and played as right back. Steady.
3. Lewis Dunk 7/10
A quiet night for the Albion skipper. Defended well and as reliable as ever.
4. Adam Webster 6/10
Strides forward so well with the ball and always trying to get Brighton moving forward. One error which almost saw Roberts score but he was saved by Sanchez