ketostix are pretty much worthless imo.
If you are new to a keto type diet, it will take time to fully adapt. Once you adapt, the lethargy will absolutely go away and you will feel great.
But you have to be tight with the diet during the adaptation phase. Trace amounts of carbs can add up if you aren't careful and can keep you from adapting or prolong the adaptation process.
Don't start the CKD with calories or fat too low. During the adaptation phase, I typically use 60% fat 30-35% protein for the first 10-14 days. And keep the calories a bit higher to make the transition smooth. After I am feeling adapted, then the actual diet portion starts. I will change the ratio to 55-60% prot , 35-40% fat. At that point I get to my desired caloric deficit.
You really have to think of the first 10-14 days as an adaptation period.
If you are feeling constantly lethargic, you are not adapted or you are doing something wrong.