It being a laptop will almost undoubtedly make that endeavour more challenging. Off hand, I can't think of a single non -proprietary internal connector from a major vendor that doesn't already have a protocol established.

If there's spare I/O, it's most likely either not hooked up, was only used as a debug header, or fused off as a feature not available on that model. If it is indeed connected to something, you'd need to find documentation on that exact model of laptop since boards can sometimes vary even within the same series (such as whether a GPU is available). Chances are, whatever your find will need a specific vendor library that may or may not work on your version of the OS.

Unlike RPi and similar devices, you won't find many consumer x86 devices that leave GPIO available and documented.

Off-hand, I think almost every LCD display I've encountered on x86 is plugged in to either a serial (for character displays) or higher-level protocol (for more complex displays)