The Blues, one of 16 ‘invited’ Category One Academies who have entered an Under-21 side to compete in the competition, are in northern group G.
This season’s Checkatrade Trophy rules mean the Everton team, led by David Unsworth, will play all their fixtures away from home.
Notts County, managed by former West Ham and Newcastle United midfielder Kevin Nolan, finished 16th in the fourth tier last season, four places below Steve Evans’ Mansfield.
Lincoln, who famously reached the quarter-finals of the FA Cup in 2016/17, are back in the Football League after a six-year absence, having been crowned National League champions.
The selection criteria for the 16 invited Category One Academy teams is to include at least six players in each starting XI who were under the age of 21 on 30 June 2017.
Regionalisation of the competition (north/south) will also be extended from the second round up to the quarter-final stage, while there will be an increased flexibility in match dates when clashes with scheduled international fixtures occur.
Among the other returning Category One Academies are Chelsea, Leicester City and West Ham, while Tottenham Hotspur, Manchester City, Newcastle and Fulham enter the competition for the first time.
“It was a brilliant competition for us last year and something that we fully bought into and embraced," said Unsworth. “We performed really well. We beat Bolton Wanderers, drew with Blackpool and got done by a dubious late penalty at Cheltenham. They were three great games and we are delighted to be invited back into it again this season.
“The Football League have relaxed the rule of the fixtures being played within the international window, so we’ve got the freedom to play on certain dates outside of that. Hopefully we can compete with our strongest team and go far in the competition.
“A lot of plaudits must go to the Football League to allow us to play in this competition. It’s a brilliant idea and, talking about the development of young players, it’s something that I believe in.”