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.
13. Jurgen Locadia 6/10
On for Maupay for his first Premier eague action in three seasons. Looked a little off the pace and one left footed shot easily saved.
14. Sarmiento 6/10
Made his Premier League debut from the bench. Looked confident and one surging run showed his quality