The way I understand it - and forgive me if I'm misguided on the subject - I've only skimmed past posts...
If the road is the property of the Roman Lakes, then they need to pay for the upkeep.
If the road is the property of the council and is a bridle way, they should maintain it in line with it's intended use.
If the council own it, and maintain it as a bridle way, but the RL want it maintained in a different way then this should come from their own budget, not the public purse. The benefits of an improved infrastructure/access point would after all (in theory) enhance their amenity - which obviously brings increased revenue.
From personal experience very clear lines have to be drawn when good causes and private enterprise meet.
Maybe they could work with the council and 'earn' some road improvements - there are many Local Authority divisions that could benefit from the fantastic facilities there - teach school children to fish is one very basic example, not to mention Local History, visits for disabled SMBC service users, the list is not exhaustive.