So what happens if Bury do fold? According to Section 3 Part 12 of the EFL rules, it depends on when it happens:
https://www.efl.com/-more/governance/efl-rules--regulations/section-3---the-league/
Without making anyone read through all of that, the upshot is:
a) Before the end of the regular season:
12.2.1 during any Normal Playing Season, its playing record shall be expunged and the number of relegation places from the relevant Division for that Season shall be reduced by the number of Clubs ceasing to be members;
In other words, if Bury fold before they have completed all 46 games (very unlikely), only one League Two club shall be relegated to the National League and each surviving club would lose the benefit or otherwise of its results against Bury. Although that would not affect Lincoln, it could have an effect on who goes up/makes the play-offs/is relegated.
b) After the end of the regular season but before conclusion of the play-offs:
12.2.2 during the period between the end of the Normal Playing Season and the conclusion of the last Play-Off Match for that Season, its playing record shall not be expunged but the number of relegation places from the relevant Division for that Season shall be reduced by the number of Clubs ceasing to be members;
In other words, if Bury fold after they have completed all 46 games but before the play-off final has been played, only one League Two club shall be relegated to the National League. With the winding-up petition returning to court on 15 May (i.e. in the middle of the play-offs), and considering the £1.6 million shortfall in what they need to survive to the end of May, this looks ominous. This possibility should give a massive lift to Notts County, Yeovil and Macclesfield.
c) After the play-offs are completed:
12.2.3 during the period between the conclusion of the last Play-Off Match and the start of the following Season, its playing record shall not be expunged but the number of relegation places from the Division in which a Club would have played but for its cessation of membership, shall be reduced by the number of Clubs ceasing to be members and, during that Season, the relevant Division shall operate with a reduced number of Clubs.
That is not very well drafted, but I think it means that if Bury are promoted to League One (either automatically or via the play-offs) but then fold after the play-off final but before the start of next season, the team finishing fourth from bottom of League One shall be reprieved from relegation and League Two will operate with 23 clubs next season. If Bury are not promoted and remain in League Two at the time of their demise, the team finishing second from bottom of League Two shall be reprieved and League Two will simply operate as planned. Again, Notts County, Yeovil and Macclesfield will be watching with great interest.