The Scottish champions went down 1-0 in Gibraltar in Tuesday's first leg.
Wales' The New Saints, who are at 0-0 after their first leg against Apoel Nicosia, have been drawn against Rosenborg or IFK Norrkoping.
Northern Ireland's Crusaders or FC Copenhagen will face Astra Giurgiu. The Danes won 3-0 in Belfast.
The return leg in Copenhagen is on Tuesday, the same night as The New Saints' visit to Cyprus, with Celtic hosting Lincoln Red Imps on Wednesday.
Lithuanian side Zalgiris and Astana are tied at 0-0 ahead of the deciding leg of their tie in Kazakhstan on Wednesday, while Norwegians Rosenborg lead Norrkoping 3-1 going into their second leg in Sweden, also on Wednesday.
Romanian champions Astra Giurgiu enter the competition at the third qualifying round, which will be played over 26-27 July (first leg) and 2-3 August (second leg).
Reacting to the draw, Celtic midfielder Stuart Armstrong said: "We'll focus on each game as it comes and we've got a good friendly tomorrow [against Wolfsburg] and an important game on Wednesday.
"We can't just turn up and expect to win [against Lincoln Red Imps]. We will have to fight for it and they will be fighting for it too."
The winners of the third qualifying round progress to the Champions League play-off round - the last knockout phase before the group stage.
Losing sides in the third qualifying round drop into the Europa League play-off round.
And winners at the Champions League play-off stage progress to the group stage with beaten sides entering the Europa League group stage.
Celtic will face Zalgiris Vilnius or Astana in the Champions League third qualifying round if they overturn their deficit against Lincoln Red Imps.