What kind of LCD is it? A 31 pin connector sounds like a sharp. If you can find the 31 pin connector and the pin outs for both the LCD and the controller then you can just get a scsi cable, cut it in two and do some soldering.
Or you can order a premade one from some one like this but they're kinda expensive.
I purchased this controller from ebay and it came with the 50pin to 31 pin connector.