Balancing lifting and martial arts?

Sweet_Heresy

Hey all,
I train BJJ and muay thai usually about 4x a week for about 2 hours at a time, and I'm following a beginning lifting program (ICF 5x5) to compliment my training...and just cause I like to lift. However I feel like my lifts are sucking and by the time I get on the mats, I'm ridiculously sore/tired and I gas way too quick.

BJJ is my priority since I am training for a competition in 3 months...so would I still be able to make a little bit of strength gains just doing the program 2x a week, and maybe doing some light kettlebell work on the 3rd day?

How do you guys do it? What does your routine look like?

(Also, 5'8" 194 lbs, female, eating around 2000 calories. Attempting to lose weight.)