I trained muay thai and BJJ for 4 years. The last 2 years of training, I started lifting for the first time. Over those 2 years, I experimented with different templates and ways to get stronger while still focusing on improving my BJJ and muay thai. The reality is that you can't improve everything at once. You need to dedicate certain periods of time to getting stronger (further away from fights), certain periods of time to becoming more technical (around the beginning of training camp) and certain periods of time to getting your conditioning up to par (all through camp).
The best results I ever got, in terms of stronger while still improving my BJJ and muay thai, were when I was lifting 2 days a week using the Starting Strength workouts. I tried lifting 3 and 4 days a week but I just couldn't ever make it work without either ending up overtraining or sacrificing my skill training/conditioning. 2 days a week with the SS workouts (or very similar workouts) are what I'd recommend for you, especially while actually preparing for a fight.
When I was training, I was grappling, striking and/or sparring 4-5 times a week, doing some sort of conditioning twice a week and then doing strength training on top of that. If you want to seriously pursue muay thai, you need to now think of lifting as something you use to improve your ability to fight, and it certainly shouldn't take away from your training. You could lift 3 or 4 days a week further out from a fight, but you still should move down to 2 times a week and eventually once a week as the fights nears.
This isn't the same as if you were a fighter who just started lifting, and you wanted to try your first powerlifting meet. Nothing bad is going to happen to you at a meet besides possibly bombing out. In a fight, bad things can happen. A guy from my old muay thai gym ended a police officer's career in a semi-pro muay thai smoker. He broke the cop's arm when he tried to block a kick to the body, and the guy apparently never fully recovered from the injury. You have to have your priorities in order to fight man. What would be worse, lifting 1-2 times a week for a few months, being fully prepared to fight and coming out of it unharmed? Or following your normal lifting schedule, getting injured in the fight and having your lifting negatively effected for the rest of your life? The choice is easy, IMO.
You will lose some muscle mass and your lifts most likely will go down (besides the deadlift). This is something you just can't avoid. You can eat a lot and rest as much as possible, but if you are truly getting into fight shape, then some muscle loss is inevitable. It's just something you have to deal with if you want to be a fighter.