In the only game to beat the weather in the whole Northern Premier League programme, Lancaster saw off Prescot Cables 3-1 at Giant Axe.
Daniel Gregson (4) put the Dolly Blues into the lead and Lee Dodgson (26) doubled their advantage from the penalty spot.
Daniel Lambert (32) pulled one back for Cables before the break but three minutes from time, David Swarbrick calmed any Lancaster nerves with their third goal.
In the FA Trophy there was heartbreak for Southport, beaten 3-1 at home by Wrexham in the quarter-final.
Joe Clarke opened the scoring on 27 minutes with a glancing header from Danny Wright’s in-swinging cross to put the visitors in front.
Chris Westwood doubled Wrexham’s lead with a header in first-half stoppage time before Jay Harris added a third goal in the second half.
Shaun Whalley scored Southport’s consolation from the penalty spot.
The fourth round tie went ahead after the Haig Avenue pitch passed a late inspection after surface water was cleared.