Hi Anthroprof and welcome to mac-forums
AFAIK, your PPC G5 and your new Mac Pro aren't compatible in that way ... I think your MB would reject the data on your LaCie as the OS structure for PPC was replaced with Intel a few years back now. I think your latest MB would be possibly use one of the new intel chips, i5, i6 or i7 ... to be honest with you Anthroprof, I'm a bit out of the loop with my iMac Core 2 Duo ... I'm lucky to have pressured Apple Aust to replace my lemon G5 just as it was on the last day of it's 1 year parts/labour warranty
You may need a friend with an older mac to help you out OR at the very worst, disassembling the LaCie ... I don't know what's involved in that, but I hope you can save your data