Quite simply (pun intended), Mass Made Simple Lite is the wrong tool for the job. And I'd wager a double Scotch that Dan John would agree.
A weight training program that's intentionally-designed to maximize strength and bodyweight gains is counter-productive when the lifter wants to lose bodyfat. It's also why I disagree with people trying to cut while running Starting Strength.
MMSL, which was published on T-Nation as "The 10 Secrets of Building Mass" ( https://www.T-Nation.com/training/10-secrets-to-building-mass ) is a solid full-body program and full body weight training routines can absolutely be killer for fat loss, but it's also designed to increase bodyweight and move heavier loads each week, and that's not likely to happen when recovery is impacted by a calorie deficit.
For sure, the MMSL/10 Secrets routine has big calorie-burners/hard conditioning exercises like farmer's walks and DB clean and presses (which are brutal by themselves, ahem, http://www.T-Nation.com/free_online_article/most_recent/the_biggest_exercise_in_bodybuilding ) but the general layout (exercise choice and volume) and overall intention of the program make it inconsistent with shooting for fat loss.
FWIW, 5/3/1 is also generally considered a "strength" program, but the template is so versatile that it's more adaptable to cutting (limited accessory work, increased conditioning, etc.) which is why I felt it was a decent alternative.
Man, if I'm a font of knowledge, it's probably Comic Sans. But thanks.