Determine how much the custom modification is going to cost you in time and cost. Is this a fast track project? so something you have already considered doing but has less of a priority on your current roadmap.
If this is something that is on your roadmap you may what to not charge as much for the fast track. Of course you need to determine this.
If one "lighthouse" company wants your system with some mods then why wouldn't "lighthouse2"? Expanding your market is a good thing.
At the same time how much is this project/mod going to affect your focus on your system and roadmap? Can you afford to delay your roadmap?

As for branching, you need to figure out a way to add this Mod as a module allowing you to easily integrate. You should be building your system in a modular manner anyways. Turn off/off features easily based on customer wants/needs.

Figure out a way to do the mod for the light house customer. :)