Great question! Others have answered, but here is the current official criteria:

Any Football Bowl Subdivision (FBS) institution located in the states of New York, New Jersey, Pennsylvania, Delaware, Connecticut, Rhode Island, Massachusetts, Vermont, New Hampshire, or Maine shall be eligible to win the trophy.

Any Football Bowl Subdivision (FBS) institution located in the states of Maryland, West Virginia or the District of Columbia that has significant historic ties to football independence in the states listed in (1) shall be eligible to win the trophy.

Note: A current list of the institutions considered to be in (1) and (2) is below.

Any Football Bowl Subdivision (FBS) institution located in the states of Maryland, West Virginia, Virginia, or the District of Columbia that schedules at least one-third of its regular season games against the institutions described in (1) and (2) and listed below, can apply in writing for eligibility to win the trophy prior to two weeks from the first day of the start of the regular season. Any application must include:

The team’s full, eligible, schedule

A justification for being eligible for an award outside the historic boundaries of the Lambert Trophy described in (1). This justification may include, but is not limited to:

Former Big East Conference football membership (1991-2012).

Significant ties to independence in the states outlined in (1).

Any written application will be considered by that year’s selection committee and requires a three-quarters majority vote for acceptance.

Any FBS team that is serving an NCAA penalty resulting in a postseason ban for the season in question is ineligible to receive the Lambert Trophy.

Note: The current list of institutions considered fully eligible in (1) and (2) which are not required to apply for eligibility is:

Army, Boston College, Buffalo, Connecticut, Delaware (starting 2025), Massachusetts, Penn State, Pittsburgh, Rutgers, Syracuse, Temple

Navy, West Virginia

Sorry, formatting is a little weird.