Beating a team from the division above was a notable scalp for Town, who were pitted against York City in the latest draw, also of the NLN, with a trip to the LNER Community Stadium set for February 12th.
Morpeth played the Minstermen in the FA Cup Fourth Qualifying Round this season, taking their higher league opponents to a replay after a 1-1 draw in Yorkshire.
Although they lost the replay 3-1, Morpeth boss Lynch is confident his side can go a step further and extend their historic run in the competition.
“I think apart from getting a home draw, this is the best draw we could have got away from home,” said Lynch, whose side have reached the fifth round for the first time in their 128-year history.
“It’s geographically close, a fantastic stadium and a great pitch.
“We are under no illusions that it’s going to be a difficult game but we’ve been there a couple of months ago, got a feel for the place and we won’t just be going for a nice day out.”
Before that, though, is a tough home clash with Buxton on Saturday (3pm), a side chasing promotion from the Pitching In NPL Premier Division.
Although Lynch is taking nothing for granted, he is hoping his squad can continue riding the crest of a wave which has seen them go 15 games unbeaten.
They haven’t tasted defeat since October, but this will be a stern test of their credentials at Craik Park.
“Buxton is another great game to be involved in,” added Lynch.
“They are at the right end of the table and although they have had a blip recently that’s not something I’ll take into account with the calibre of player they have.
“I know we will have to continue the level of performances we have been because it will be a tough game.
“The squad is in a great place at the moment and it’s another game we are relishing.”