in one way running will first strip your body of excess fat, raid your glycogen stores in the very first instance… if its anything like the basic training i went through in the military, they wake u up at ungodly hours which worked wonders for getting body fat down to sub 10%!
however, without the proper caloric intake, you will lose muscle mass yes. if you eat more protein this will be negated in most cases. however man, dont sweat it, if its what u wanna do, crack on head down into it, eat as much as you can as often as you can and youll be the star cop in no time!
Make sure you feed your body, especially before early runs. Carbs will be your friend at this time, the quick energy source will aid in supplying fuel and replenishing your glycogen stores. Lifting during this period, especially when consuming an adequate amount of calories will help stave off muscle loss by giving your body a stimulus telling it, oh shit, I still need muscle to fight off bear, or fat women in the buffet line.
Long story short, eat and give your body a reason to maintain its muscle mass.