I am pretty sure I need exercise as my sedentary energy need is about as much as a barely enough meal if I do everything right, avoiding (or seriously minimizing) everything that isn’t a proper protein source, among others… And I regularly want to eat more than that and mess up this and that…
I don’t lose fat either way but I want to avoid overeating at least as that isn’t fun.
But I never lost far just because I exercised more, ever. It would be possible but I never was THAT active and I can easily eat twice as much if I need it (even if I don’t, actually, maybe not on keto every day… ;)). I need to focus on eating as little as I comfortably can - and exercise too. But I actually lost without exercise in the beginning, no wonder, my energy need was higher then and low-carb was novel and not eating without a proper urge was more natural as I was more driven… Good old days, years before keto.
I actually need strength training as I eat much anyway, I want to get some muscles out of it at least! 
And muscles are pretty and useful.
I exercise for health, energy and similar reasons. I stall either way so it would be pointless to do it for fat-loss. It doesn’t happen.
My SO is the one (on high-carb but it doesn’t really matter) who needs an active lifestyle to avoid fat gain (he gains easily so his 2 weeks long not very active holidays in December always resulted in sudden and noticeable fat gain. he is like me, activity or lack of it does very little to his energy intake or food choices unless we are active all day so the deficit would be huge without an unusually high-cal day). So he has that, a somewhat active lifestyle. I am mildly active, I only walk an hour a day at most, tiny runs, weightlifting… It can’t help much with fat-loss unless I do my eating VERY well. Like, carnivore OMAD with only satiating items, that should cut it. But activity makes my minuscule energy deficit a tad bigger… Or at least my tiny muscles very, very slowly bigger, that helps too, eventually… 
So nope, exercise doesn’t automatically cause fat-loss. Just like keto or IF don’t.
But it may help, it may have zillion other benefits… And for some, it may be needed for fat-loss (or avoiding gain).
But I’ve heard exercise goes against fat-loss for some as they get more hungry or maybe their body decides to do something else than losing fat…?