No.  Assuming that the payment is entirely voluntary and is not part of an understanding that the participants in the luncheon will rotate the $100 cost among themselves each month, the payment should qualify as a charitable contribution for which no goods or services are received in return.  Under the quid pro quo rules the charity would have an obligation to give a substantiation letter for a payment of more than $75 if significant goods or services were received in return for the payment.  That statement would have to state the value of the goods or services received in return for the payment. But since everyone gets the lunch in your situation whether or not they contribute, I don’t think this can be considered a quid pro quo payment.

A charity is not legally required to give a substantiation letter for a cash contribution (for which nothing is given in return) of any amount.  A donor must receive one, however, in order to claim a charitable contribution deduction for a gift of $250 or more.  Without a contemporaneous substantiation letter, a donor may not claim the deduction.  In your case, the donor could claim the deduction even if he or she contributed for three or more lunches during the year because the requirement applies only to individual payments, not a series of payments, that are $250 or more each.  (See Ready Reference Page: “IRS Requires Substantiation of Contributions”)

It is always a good idea to provide the letter, however, with the statement that no goods or services were received in return. It is good donor relations, and can help avoid questions if the donor is ever audited by the IRS.