The visitors were having the better chances in an even game as Matty James picked up the ball on the edge of the area and drilled a volley just over the bar.
Brighton finally clicked into gear after 30 minutes when Andrea Orlandi's corner found Inigo Calderon who headed at goal, but Danny Drinkwater cleared it off the line. Liam Bridcutt then fired a volley towards the net but Kaspar Schmeichel made the save.
Leicester responded and went within inches of taking the lead as Andy King saw his effort well saved by Tomaz Kuszczak, who tipped the ball onto the crossbar and over.
After the break, Leicester began to up the ante and came close twice as Liam Moore fired over from close range while King forced Kuszczak into another good save down low to his left.
Brighton could have taken the lead through Leonardo Ulloa but he somehow missed the target from six yards out after he latched on to LuaLua's cross into the area.
This was to cost the home side as the Foxes took the lead in the 73rd minute as James fired them into the lead, slotting the ball past Kuszczak from close range.
Just as the visitors looked to be heading for the win, LuaLua struck in the 88th minute as he raided down the left and cut inside on his right foot before firing an effort past Schmeichel to earn a point for his side.