LVDS (or more properly, FPD-Link) is a mostly-universal standard, although the bit packing sometimes varies and the pinout always varies from panel to panel. But you can usually get there from here with some bit-mangling and a connector change. It is very common for a bare panel to take some normal variant of LVDS, although then inside the panel's controller it may break this out to mini-LVDS or some other somewhat more muddled standard.
You can buy a "universal" x-to-LVDS controller, which uses the most standard 4-lane 24-bit packing scheme (I think this is JEIDA packing, but I can never remember whether it's that or VESA - two competing standards)
[EDIT] VESA is the more common scheme. Typically if these are sold as being "for" some specific panel, they will include a cable with converts your specific panel connector to their generic pinout, and will load the board's EDID EEPROM with the proper values for the panel. Sometimes voltage levels for the LVDS interface are also varied (there are standards for 3.3V, 5V and others). They also may include a proper backlight driver for your panel (CCFL or LED, 2 tubes/6/8/12 strings, etc). But the core data is mostly universal.
In the high-res laptop screens though, it is becoming very common for the interface to not be LVDS but instead eDP. This has come about with higher-resolution, higher-refresh-rate panels, since LVDS is somewhat limited in maximum pixel clock speed. In desktop monitors they get around this by running multiple LVDS channels for subsections of the panel, but the number of extra wires would be undesirable in a notebook application where the wire bundle must be routed through the hinge etc.
For your application (as I have read a couple of pages of the linked thread), it all comes down to what the panel actually wants for a signal, and how it uses it. I didn't look real hard but it didn't look like anyone had taken a cover off those displays, so it's hard to say anything else.
If you need any help with the design effort let me know
[Edit] How vague my second-to-last paragraph was. Distracted... What I meant was, if you are looking to drive the panel with individual "generic" driver boards, you will need to make sure that this is how it is driven internally (i.e. with individual paralleled LVDS channels), and the only real way to do this is to open it up and check. Then after you know the physical interface you need to know how that maps to the screen - whether it's interlaced, or halves/quadrants, or what - since ultimately your host system has to split the image into these parts and send each part over an individual interface.Edited by moddermike - 8/7/13 at 1:51pm