Combining very low-fat with very low-carb can be dangerous resulting in something called rabbit starvation, sometimes called protein poisoining - but it's not the protein, it's the abscense of fat and carbs. It's called rabbit starvation because it was seen in pioneers during wagon trails when provisions ran out and the only source of food was rabbit (very lean, no fat). It's said that people died faster on a diet of just lean protein, than if they had no food at all.
Are you in danger of rabbit starvation? Unless you're really stubborn, probably not, because if you get severe unpleasant symptoms, you're probably going to stop and see a doctor (hint, if you get severe unpleasant symptoms, try eating some carbs and see a doctor).
There was a diet that a women invented and "sold" online (and didn't follow herself. because the before and after photos of her and other members were faked). The plan was a very low-carb version of Atkins and she told her followers that being sick (nauseous, light-headed, headaches...) was good and a sign that the plan was "working." At least one person actually died (heart attack, I believe - probably from electrolyte imbalance).
I'm not purposely trying to scare you, just pointing out the danger in trying a low-carb diet that is virtually absent of fat and carbs.
How many carbs (or fat) grams are necessary to be safe? I'm not sure there is an exact number, so just be careful and listen to your body. If you feel like crap, there's a good chance somethings wrong.
I personally, don't thrive on Induction. I get sick (and do not get better after two weeks, so it's not just "Induction Flu." I just keep getting sicker - unless I eat so much fat that it slows my weight loss).
I really love my doctor for suggesting I try low-carb, but warning me not to go "too low" (though admitting he had no idea what was too low). It made me ready and willing to experiment.
The book didn't really focus on the possibility that induction could actually make some people ill, and that the "cure" was eating a bit differently. I realize why, it would have confused a lot of people. And it's also very possible that my reaction is very unusual and Dr. Atkins never (or rarely) encountered it in his patients.
I'm just saying "experiment" because your ideal calorie/fat/protein/carb ratio may be different than mine or someone else's.
Right now there's no way ot predict which type of diet will work best for which people.
Some day there may be, but right now there's only trial and error, so you're left with being scientist and lab rat. That's horrible science, but it's all we've got.