I actually train and fight Muay Thai and lift as well.
There are a variety of things you can do for gaining strength and it doesn't only have to be weightlifting unless ofcourse weightlifting is an interest of yours. If you're after strength for the given sport without care of how you get it, then explore Ross Enamaits information in his books and website.
He's an awesome guy and very helpful.
Like some have alluded training your body and not "muscles" is what you have to aim for.
"Muscle" training is for bodybuilders or rehab not for athletes.
You need to condition your body at the chosen sport the specific way for the sport.
Sure some exercises are great and have higher tranfer over success but do NOT train like a bodybuilder - one part a day movements.
You also have to forget about the idea of how you look and focus more on how you perform.
At 110 kilograms I looked buff and mean but at 98 kilograms I maul even the bigger guys with speed, more power, fitness and endurance even though I look scawnier.
I don't have bulging biceps and pecs but something that the opponents mention after fights is that they thought I was fairly strong compared to what they're used to and my look was deceptive.
Train hard in class. Getting your technique right will help too. What does that mean exactly? Well it means learning how to switch your body "ON" at the right time. Making sure your CNS fires right which then makes your muscles fire right.
For example it is no use having an excellent CNS activation in your pecs, shoulders and triceps during a punch if your biceps, lats, rear delts etc are firing at the same time antagonising the movement. That's not very economical at all. So slowing down, reducing your power and working your technique until it is perfect (well close to it) and then adding power and speed will work wonders.
You will eliminate negative antagonism which will tire you and rob you of power and speed.
I see some supposedly really strong guys in the gym buckle when I throw a 66 kilogram fighter in with them to train. They can't believe how hard he hits.
Likewise, western fighters often freak out at the power a small thai guy has. They forget that their techniques are usually flawless as they have learned to do it from a very young age.
They can throw powerful kicks and punches all day long without getting as fatigued and that is largely because of economy of movement and perfection of technique not because of scientific strength training protocols designed in university labs lol.
Whoooaaa... sorry.... end rant.