The young Magpies travel to the LNER Stadium for their final Northern Group E fixture, unable to progress into the knockout stages after losing on penalties to Doncaster Rovers, following a goalless draw at the Eco-Power Stadium, and a 2-0 defeat against Barnsley, who competed in the Championship last term.
Brookwell, who has captained United's under-21 side on a number of occasions since joining from Liverpool in the summer of 2021, expressed his excitement in taking on the League One outfit and believes the squad have gained a great deal of experience during this year's competition.
The Wigan-born youngster told nufc.co.uk: "The lads are looking forward to it just a bit more because it's a better test for us. We like to find out where we're at, both as a team and individuals as well. We always look forward to these kind of matches.
"We've missed a couple of chances where we could've capitalised in the group games. We've competed well but I think we just needed to have more belief and push on to try and go for the wins.
"It's always a good way of learning and showcasing yourself, testing yourself against a strong level of opposition. Whether we could go through to the next round or not, those things would stay the same.
"It's been class playing in the stadiums. Barnsley's ground was great to play at and having a lot of fans there adds to a good atmosphere. They have been a test but we've played well in both and it's just a case of trying to push on even further against Lincoln."
Newcastle's second-string are currently unbeaten in their last four Premier League 2 matches and recently recorded a 2-1 win against Aston Villa Under-21s on Friday night - their first away victory of the 2022/23 season.
Brookwell was delighted to come out on top against their Villans counterparts and is hopeful United's youngsters continue their unbeaten away run in all competitions ahead of facing Mark Kennedy's Imps.
The 20-year-old added: "The mood in training has been good at the minute. We've been doing well in the Premier League 2 and the camp is really positive.
"We need to try and carry on what we have been doing in the league in this competition which is easier said than done. It's a case of trying to do what we've been doing lately on Tuesday night.
"The lads were buzzing with the first away win of the season. We had to dig deep at the end but it felt really good at full-time knowing we'd got the win."
Supporters can attend Tuesday night's Papa John's Trophy clash at the LNER Stadium, with tickets available to purchase on the day from the Visitor Window at Lincoln City's club store.
Away fans will be situated in the North East Stand, which is covered.
