If I want to improve insulin sensitivity by going onto a keto diet for a few weeks will I lose muscle due to lack of carbs?

You lose muscle only as a last resort, muscle is important and energetically expensive to make so you have to be a bit crazy to put yourself in a position where the body starts eating muscle for survival.

Easier to happen on a carb diet then a keto diet.

On keto you usually have to go below 5% before the body starts to burn muscle for fuel.

Easy to do on carbs just eat lots of very small meals but staying calorie deficit so your body has no chance but to tap into its fat reserves!