I myself am nowhere near to what one might call an expert in the field of martial arts and lifting, having only about 2 years of Thai Boxing and about 3-4 years of lifting done so far, but my piece of advice would be that you need to find out what works the best for you. In the terms of boxing, you can really push your recovery and all as long as you are not burning yourself out, because its very likely that you will still make gains in the terms of technique even if it might slow down your gains in the S&C department.
When it comes to lifting, you need to remember that you build most of your strength recovering. Therefore it might be actually more beneficial for you lifting less, because boxing and lifting is already pushing your recovery to the limits and if you increase the lifting from there on its more likely to actually slow down the process and eventually to burn you out.
Tracking your progress in boxing can be a bit more difficult, though if you feel like shit in every training and feel like you just ain't making any progress then it seems like a pretty obvious of an indicator that you are overdoing your lifting or just otherwise pushing your recovery too much so you don't have the energy to focus on your skill training.
Tracking your progress with the iron in the other hand, is very easy. Just pick up a notebook and write down the numbers every time you lift. Get a progressive program from the internet or just make one up by yourself, doesn't have to be complicated, I try to add 5lbs to all upper body movements every week and 10lbs to all the lower body movements every week and I've been doing fine so far.
Don't start too high and you will most likely get bigger and stronger and decrease the risk of injury. If you are really pushing it in the gym, having off week like once in a month or decreasing the weights a bit like every 3-6weeks might be a good idea, but yet again, you have to find out what works the best for you.
I myself like to lift twice a week, keeping both sessions very brief (about 30mins which includes the warm up) with about 4 main lifts (squats, deads, rows, upper body presses mostly), performed in supersets, and some core work with maybe occasionally throwing in some extra work for some certain muscle group that is lagging behind.
You say you've been doing power lifting kind of training so far, which is the way I like to do it too. In my opinion doing bodybuilding programs made for big roidpumped beasts will only exhaust the shit out of you and won't let you make the most out of your skill training, not to mention its probably not going to make you perform any better in the ring if you are ever to have a fight.
Remember to keep on stretching after every session to keep yourself loose and flexible, cause I feel like one stiff piece of shit after every heavy lifting session unless I really put some focus on my stretching.
Get your goals set and your nutrition and recovery in order and you are pretty much ready to go. Most important thing of them all is that you learn to feel out how your body reacts to different kinds of training, if it works for you and you are happy with the results, fine, stick with it and be happy, if it doesn't work, ditch it or think about what went wrong and make the required changes.
If you injure yourself, its probably going to keep you out of the gym and the weight room, so keep that in mind when your joints desperately scream for some rest but you feel like going in the gym and throw some weights around.
E: Eww shit, didn't even notice the original post was a bit old... Well, hope somebody might benefit of this .