Is it possible to lose fat and build muscle simultaneously?

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Hello all!
So, here's my situation. I am a 5'4'' female, and I currently weigh ~146lbs. My goal is to get down to around 130 lbs. However, I know I need to lose fat, but I also (really!) enjoy weightlifting and I don't want to give up my strength in order to thin down first and then try to rebuild. My intentions right now are to restart Insanity and add in a few days of weightlifting to keep up my strength.

Does anyone have an additional workout plan (and diet plan!) that they would recommend for this? If it is even possible?

Any help is appreciated! Thank you!

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