The winner over the two legs will play Serbian giants Partizan Belgrade in the next round.
Gibraltar is European soccer body UEFA's newest and smallest member after being admitted in May last year following a 14-year battle during which they faced fierce opposition from Spain.
The Gibraltar Premier League has eight teams, including one called Manchester United. Lincoln have won for the past 12 seasons.
The British overseas territory, whose sovereignty is disputed by Spain, beat Malta 1-0 last month in a friendly in Portugal. That was their first international victory as UEFA members after two draws and two defeats.
(Reporting by Alan Baldwin, editing by Stephen Wood)
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