Buy the proper Lexus wiring kit, buy a cheap car trim removal kit off ebay to make life easier, set aside a morning and follow the destructions :
http://www.toyota-tech.eu/aimuploads/%7B792E8204-B20E-434E-AB7C-0FB195D08A09%7D/Towbar%20wiring%20kit%20PZ417-K2561-00%2013PTOWBWH.pdf
It's not difficult but you just need to be patient and prepared to remove most of the boot trim and floor panel etc - get some tape and stick the bolts to each part they came from as you dismantle everything so you don't get confused when putting it all back. Took me about 2hrs going slowly but that was 7 pin not 13 but the time is all in the removal of the trim rather than an extra couple of wires.