The Linnets will face Aveley, currently second in National League South, in the second qualifying round on Saturday, September 16.
Wroxham face a trip to Barton Rovers if they can get through their replay at Canvey Island on Tuesday night.
Gorleston have an away tie against the winners of the tie between Bedford Town and Walthamstow.
The Linnets return to action on Tuesday night when they host National League North leaders Brackley Town.
Lynn will be looking to make it three games unbeaten after their goalless draw at Farsley Celtic at the weekend. Manager Mark Hughes will be without the suspended Tom Clifford and fellow wing back Kian Ronan, who is on international duty with Gibraltar.
Despite a mixed start to the new season, Lynn haven’t been beaten at The Walks, although the visitors are unbeaten in their seven league games this campaign.
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