You can definitely lose fat and gain lean mass at the same time - presuming that your diet and exercise regimen is not already top notch, and I know it's not.
Just clean up your diet (get rid of all poor nutrient sources, stick with good carbs, good fats, and varied protein sources). Make sure your rep range is 8-12 for most (90%) of your lifts, and reduce your rest periods to < 1.5 minutes for lifts in the 5-8 rep range. Add in a good bit of cardio, start doing heavy cleans and snatches three times a week. Get in the gym to lift 4 days a week. Sleep properly. You'll be lean and jacked if you stick with it.