Oh, I just reread and realized I missed something. I thought you were buying the harness for your LS-30's. Since that's not the case and you are actually looking for harnesses, I can tell you....you are screwed!

I have 2 LS-30's and really like them (I use them for my primary controllers, so I guess I don't have anything else to compare them to). Anyway, they didn't come with any wiring harnesses. There were some wires soldered onto the joystick switches, but nothing connected to the rotary switch. I found that there is NOWHERE to buy the stupid harness. I eventually found a guy that posted a guide for how to make a Happs 49 way into a rotary stick and was selling kits. He sold me a few connectors for a good price, so I built my own.
I don't have the info at the moment, but the connectors are basically just standard 13-pin PC female header blocks. I can't remember if they are 0.1" spacing or not, but you can always just measure to be sure. These things are available at Mouser or DigiKey once you figure out what the specs are.