I'm about to get my own mac laptop, but I got LimeWire on my parents computer, who never use LimeWire. I was wondering how I would install it on my computer without having to pay again. Does someone know anything about this?

For mac you can simply copy the program across. But make sure you keep the entire contents of the incomplete folder also (Open LW on your new comp & set up the preferences such as downld location, then close it. Then replace the incomplete folder with the one from the other computer.)
Otherwise you can re-downld it from the official site if you know the email & if it's still eligible for updates & downlds (within 6 months of purchase) HERE (click on link)