There are two different kinds of internal 50 pin SCSI connectors, big and small (high density?). Yes, the one on the LC HD is standard, but if you bought a recent USB SCSI converter, it's probably the -other- standard.
Luckily they are electrically identical so you should be able to find a 50-50 converter on ebay for a few bucks.
You say you have a "USB 50 pin adapter" but you don't realise the drive is SCSI ... so what did you actually buy?