There are a lot of options, and its a very complex topic. It depends on the type of training, the person, the amount calories, etc. etc.....
But heres a little reasoning.
The point of low carb is to cut fat. You'll want to be in a caloric deficit, and higher protein/fat will be helpful in maintaining muscle during this time.
The point of refeeds, or cycling carbs like you would be doing is to prevent your body from adapting and slowing the metabolism and burning muscle.
So if your refeeds are adequate during the lowcarb week, you dont need to cycle up the next week. But if your first week didn't have refeeds, or had some serious depletion workouts, then cycling up might be a good idea.
Also its going to depend a lot on your goals and your current body. If you have a lot of fat to lose, you'll generally want to go for longer periods on lower carb/calories. If you are already lean, and are trying to get really cut, then you'll need more carbs, and refeeds more often.
And then your training is going to affect it a lot. I see you already have an idea about this as you didn't try to pair low carb with HIIT, but the frequency, and volume of your weight training will be a factor as well. It will be really complex, so my advice would be to read up on carb cycling and realize that there arent any real clear guidelines to follow; yet.