My case is quite similar in overall details to yours- diagnosed about 3 months ago, immediately went on LCHF, lost 20+lbs, not on meds, What happened with me was that I was losing a 1lb or even 2lbs a day when I started at 200lbs, but then I slowed down when I got to about 175, and now I'm losing about 1lb a week, being 168lbs today. My energy levels used to drop quite a lot and I had trouble walking up stairs to go to work etc, but I started adding some walnuts/ almonds and sunflower seeds to my diet, and it really took the edge off the tiredness. I find that as long as I have a boiled egg, or some sardines, and some nuts, then I can pretty much just eat steamed veg to fill up, and I have quite a lot of energy- certainly more than I had pre-diagnosis.
So for me, when my weight reached a sort of 'natural plateau' the exhaustion decreased, and then having nuts or sunflower seeds helps further. I also drink a lot of tea with no milk during the day, but I don't know if that last part is as healthy. Pre-diagnosis, I could go through 6-7 espressos, a can of monster and a litre or two of tea in a day, but I don't need it now.
It might be that your tiredness might be like mine- a bit of a reaction to cutting so much weight so rapidly. If so, then hopefully it will get better as your body gets nearer to, say, BMI 25 or equivalent. Make sure you're getting your nutrients, and maybe try some almonds and darjeeling as a little pick-me-up.