I'm not going to comment on the legalities of tenant-landlord laws that might cover this situation. I will leave that up to those that know more than I do. But I will say that there appears to be something not legal about the town's actions in this situation if the information posted is true.
It's hard to believe that 25 years ago (or so) the town could have allowed a private non-profit to build on public land in violation of the Illinois Municipal Code with a letter and a handshake. That would mean that there is no ordinance, no hearings, no written lease, no contracts, no liability insurance guarantees, and the list goes on. Who gave the authorization and wrote that letter? And who now is telling the non-profit to vacate and under what authority again. So where and how was this decided?
OP, were you part of the non-profit when the deal was made or is your information from hearsay? Have you researched the records to find any to any official action by the governing body? And how was the non-profit notified that they wanted you to vacate?65 ILCS 5/Art. 11 Div. 76 heading)
DIVISION 76. SALE OR LEASE OF REAL OR
PERSONAL PROPERTY
(65 ILCS 5/11-76-1) (from Ch. 24, par. 11-76-1)
Sec. 11-76-1. Any city or village incorporated under any general or special law which acquires or holds any real estate for any purpose whatsoever, except real estate granted to a municipality as commons by a grant which has been confirmed by the government of the United States, has the power to lease the real estate for any term not exceeding 99 years, and to convey the real estate when, in the opinion of the corporate authorities, the real estate is no longer necessary, appropriate, required for the use of, profitable to, or for the best interests of the city or village. This power shall be exercised by an ordinance passed by three-fourths of the corporate authorities of the city or village then holding office, at any regular meeting or at any special meeting called for that purpose. However, the corporate authorities have the power to authorize any municipal officer to make leases for terms not exceeding 2 years in such manner as they may determine.
This may all be water under the bridge but I don't think so. This is not a private landlord-tenant matter and municipalities have to follow the law.

