Build the muscle and burn the fat!
I hear all the time .. “I want to build *lean* muscle” … well muscle IS lean body mass; there is no such thing as building fat muscles. Build the muscle & burn the fat. I know, easier said than done!
And yeah, sometimes this means the scale will play tricks on you as your body composition is changing (as you start to gain muscle & lose fat).
So take pics, measure & be patient. And yes, building muscle helps burn the fat faster (because the more muscle you have, the more fat you burn).