I'm going with custom display, as I have no idea if its graphic, character, digit, TN, STN FSTN etc..
Given that there is more than jsut an LCD on that board, one can assume that some of the 11-wires are for non-LCD things, like switches, LED's etc.. So I'm going with a serially controlled display. Once you've identified the power lines, the ones for that switch, and the power for the LCD backlight, youcould probe the rest with a logic analyzer to see whats happening, if there really is a clock and data line.
I suspect it is a lot of work for little gain - but I have done this sort of things before, purely because I dont' like throwing things out and some displays are really rather nice. Depends on what equipment you have to hand (a $10 logic analyzer will do just fine for this sort of thing, although it might not have protocol decoding, which isn't always needed) and how much you wish to re-use it.
If you're just starting out it might be a lot of effort, but you could always just stash it in your parts bin should you wish to come back to it at a later date. Be warned, that sort of habit can be dangerous... I have over 35 displays waiting for projects to use them
Do you have a link to the product it came from? I googled but found nothing with a display.