10 lbs/month is about the quickest you will want to go and it can't reasonably be done, in my experience, without adjusting diet. It is super difficult to try and only workout to a lower weight.
Keto (Atkins, LCHF, whatever you wish to call it) obviously works, but I've found that it is too restrictive. Whenever I need/want to lose weight, I always return to keeping food and activity logs (FS is as good or better than any I've found) and Calories In < Calories Out (CICO) work the best for me. I use a Fitbit for my activity.
"Fat, drunk and stupid is no way to go through life, son." - Dean Vernon Wormer, Faber College, Animal House
"I was sick of being fat..." - Drew Carey