It would help to know the make and model of the machine in order to best advise, as not all machines use the same type of cabling. To momoside's point, checking the owner's manual that came with the machine is a great start; it -should- have a customer service, technical support and or sales line you can call for replacement parts.
If that's not the case and/or if for some reason you don't know the manufacturer, I would take the current cable with you to an exercise equipment store (Big5, Dick's, etc) or a hardware store (TrueValue et al) and have them help yo locate replacement cabling.
A final option would be to go to your local gym and ask them who services their equipment and if they could refer you.
I checked online and could not locate any place to find replacement cable for a lat pulldown machine. It really depends on what model you have. I suggest you look in a manual if you have one and call to see if they sell replacement parts for it.