You probably need to probably approach it from a different angle, what are your goals? I want to build muscle and bulk up? I want to burn fat and improve body composition? I want to lift 400 lbs? or I want to run ultra distance? Then you can go ahead and decide what work outs are the best. If you are doing Keto or CKD or some variation and working out, you need to understand how the body performs at different intensities on low carb.

Watch this video

http://www.youtube.com/watch?v=NqwvcrA7oe8

The above video sums up very well from what you can expect, remember its not a theory but Dr Attia experimented with himself.
Now to the basics of Keto and exercise, your ketone levels or keto adaption won't yet impact the athletic performance, the intensity of the exercise will dictate what fuel is used. Higher the intensity, the body will start using more carbs as fuel because your body is not used to utilizing fats at higher intensities. Look up RER/RQ, which tells you if the body is using carbs or fats. You have two options early in the keto diet.
1)Cut down on the HIIT ( HIIT is not very beneficial for low carb, because you don't have ton of carbs to burn at high intensity to force body in to burning more fat). Initially when I started low carb, I couldn't even exercise for first 3 weeks, my body started burning predominantly carbs starting at like HR of 100. I choose not to carb reefed but to force my body to improve fat oxidation. Right now I burn predominantly fat even at 85-90% of my Vo2 max. This approach is more like short term loss but long term gain. I can get through intense work outs and recover from them very fast with out carbs.
2) The second option is to reefed or eat carbs before HIIT work outs, with this you won't have problem getting through your work outs now. But, how ever your RQ/ fat oxidation won't be as high as the first option. Your body will continue to use carbs because its preferred fuel for the body if present.

There is no right or wrong approach, its a matter of choice. For me the first option made sense as my goals were to increase fat burning and also I am more focussed on resistance training because thats the best combo for burning fat along with a ketogenic diet. You need to figure out what your goals are and adjust the workouts and diet accordingly. I choose to adjust my work out routines based on my diet not the other way round. You can choose to adjust diet based on your work outs if thats your goal. After 6 months, it doesn't matter for me because I burn fat at high intensities. Not sure where you are but you can get RER/RQ tested, I do metabolic tests every 3 months.