The lender has a legitimate concern and wants to see if there is a written maintenance agreement for the road. My assumption is that your subject is located in a small development with an informal agreement and no HOA dues; otherwise, as a rule, road maintenance is included in the typical HOA dues (please post if your subject does pay HOA dues but the road maintenance is not included in those dues; that would be unusual in my market).
However, although the lender's concern is legitimate, it isn't your problem (kinda). As a rule, if the roads are private and there are no HOA dues, I would have asked the borrower/owner if there is a written maintenance agreement. If not, I note in the report that the there is no formal maintenance agreement for the..... (you name it here) and suggest that the lender obtain the agreement from the appropriate source (with the strong implication that such source is not me :new_smile-l: ).
The appraiser is always the easy one to ask for something when nobody is sure where to get it and it relates to the property. Your client is going to have to get it from the borrower (IMO), or, you may consider providing an addendum that no private maintenance agreement was provided to you and leave it at that.
Sometimes, a lender will not loan if there isn't a formal agreement in place. It can become nasty among the neighbors (depending how many have to sign-up) if there are hold-outs. I've heard of cases where the one property owner will take on full responsibility for the maintenance just to get the loan.
Like you, I learned this the hard way. And, like me, chances are good in the future if you are doing another private road scenario and there are no mandatory HOA dues, you'll ask if there is a formal maintenance agreement prior to completing the report.
Good luck!