The visitors convincingly defeated Doncaster in the opening round while the home side needed penalties to see off the threat of Blackpool.
Match preview
Lincoln City suffered a first league loss of the current season as they were thrashed 4-0 by Peterborough at the Weston Homes Stadium on Saturday.
Two goals apiece from Jack Marriott and Jonson Clarke-Harris left Mark Kennedy and his team red-faced at the sound of the full-time whistle.
Consequently, The Imps have dropped down to 17th in the League One table, albeit only a point shy of the top half and a further two behind the last playoff place.
Lying in store next is a clash versus an opposing outfit who are yet to suffer defeat in any of the previous five meetings between the teams.
Having seen their five-game unbeaten run on the road come to an end last time out, Tuesday's visitors now set out to avoid consecutive defeats away from home for the first time since April.
Barrow picked up a second straight league win courtesy of a narrow 1-0 victory over Harrogate in Saturday afternoon's meeting between the sides.
Josh Gordon opened the scoring in the final minute of the first half and that was enough to hand Pete Wild's men a well-deserved three points.
With 12 points picked up from a possible 15 so far, The Bluebirds currently sit third in the League Two table, one point behind Leyton Orient at the top of the pile.
Off the back of three wins on the bounce in front of their fans, Tuesday's hosts will be looking to put on another dominant display on home turf.
Barrow EFL Cup form:
Barrow form (all competitions):
Lincoln City EFL Cup form:
Lincoln City form (all competitions):
Team News
With six direct goal involvements in his five league outings for Barrow this term, 26-year-old Ben Whitfield is definitely one to keep an eye on.
Defender George Ray is yet to feature for the hosts since pulling up with a 14th-minute injury against Bradford City earlier this month.
Following a humiliating defeat against Peterborough last time out, Mark Kennedy could be tempted to make some alterations to his lineup for this one.
The likes of Sean Roughan and Charley Kendall had to make do with second-half cameos in the aforementioned game and will be pushing for a start here.
Barrow possible starting lineup:
Farman; Warren, McClelland, Canavan, Brough; Neal, Foley, Gotts; Kay, Gordon, Whitfield
Lincoln City possible starting lineup:
Wright; Robson, Poole, O'Connor, Eyoma; Sanders, Sorensen, House; Scully, Hopper, Garrick