The Imps will head to Tranmere Rovers or Burton Albion in the second round of the Carabao Cup.
A power cut around Prenton Park means Rovers and the Brewers have yet to play their first-round tie, which has been rescheduled for Tuesday 19 August.
City booked their place in the second round with an impressive 3-1 win at Harogate Town on Tuesday night.
The tie will take place in the week commencing 25 August.