I do weights before cardio as a rule. But ... (and this is the exception that proves the rule) I do HIIT before weights. I'm keen to train my body to burn that fat so I want to do the HIIT as well as I can.
I don't do HIIT and weights on the same day. If I'm doing weights then I'll do some non HIIT cardio to warm up - perhaps 10 mins on stationary bike or treadmill - and then maybe another gentle 10 minutes after doing weights to cool down.
I've been reading the BfL site and that's what it says there, but I figure I don't do anywhere near as many sets of weights as it suggests so I'll be ok! Plus I like to take Thursday off the gym because of extreme kickboxing so that only leaves me 4 gym days to do my 4 day split! I think I'll try HIIT-ing on Weds and Fris. We'll see how pooped I get tonight! I'm just looking forward to a good "after" picture!
I would think your kickboxing would count as your cardio - I wouldn't want to attempt any weighted LBWO after hitting one or more lower body 10s in case I damaged something (on me).