That is a tough situation. Cortisone is likely to push your blood sugar up. If you take insulin to counteract this rise, it may make you gain weight. On the other hand it may just push the blood sugar back into the liver where it came from. I think you may struggle to get the fat burning, ketone burning aspect of low carb working while you are taking cortisone. But that's just a theoretical answer, I don't have direct experience of it. Hopefully someone else does... bump.
Cholesterol. Well on la ow carb diet you would ordinarily not worry about total cholesterol, but instead look at things like your HDL cholesterol ratio and your triglyceride ratio. These results are what you get when you do a "full lipid" profile at your doctor or hospital. Also remember that eating fat in your diet does not raise your blood cholesterol, that's a myth. What causes your blood cholesterol to rise is if you have excess blood glucose (from carbs in your diet) and then your liver tries to turn that into fat for storage. And it can only make VLDL cholesterol for this, which is the worst kind.
However on a low carb diet plus steroids it might not be so straightforward.