I'd encourage you to read up on CKD/TKD as much as possible. I don't know anything about the Lutz plan.
A regular CKD is probably best done with an intense weight lifting regime, at the intermediate level. At the beginning level, you're not really lifting heavy/intense enough to deplete muscle glycogen sufficiently to warrant a weekend carbload. At least, this has been my experience.
A TKD is usually my preference for low carbers, because it allows you to get your carbs for lifting (best taken before and/or during lifting, not after), and then return to ketosis soon after the workout. This seems to work best for people who are "carb sensitive".
Another approach I have tried that worked well, was a CKD/TKD hybrid. TKD during the week, and then every other weekend I had one refeed (carb load) day. These refeeds are normal protein (usu. ~1gP per pound of LBM), LOW FAT (no more than 50gF total),LOW SUGAR (no more than 100g) and then high carb, up to about maintenance calorie levels (or as much carb as you can cram in with the above restrictions).
It's been my observation that the only ones who tend to do really well on a traditional CKD with the big ass weekend carbload were advanced male lifters. Beginning level men, and women, seem to have more issues with bouncing up and down the scales with long carb loads.
Really, if you want to keep your muscle mass and lose fat, the best things you can do are to maintain a caloric deficit (and for me this is easier/more comfortable to do on a lower carb diet, usu. TKD style), and lift HEAVY. This means "heavy for you", basically lower rep/higher weights. You may want to research this further, and consider trying this with your bowflex.
HTH! (Hope This Helps!)