I’ve been using IF and fasting protocols for several years.
Working out fasted is probably a good idea, even if it’s only IF (say you work out at 0800 and don’t eat until 1600 or so).
Working out during a long term fast is probably a good idea as well. I’ve done it lots of times (ran 12 miles on day six of a fast, that kind of goofy stuff) and I’ve never experienced muscle loss as a result.
You should listen to your body BUT, sometimes the body will lie.
Here’s what I mean by that. I often use a 3-5 day fasting protocol, sometimes, on day 3, I wake up and my body is SCREAMING “get back in bed, you don’t have the energy you need, stay in bed!” But I’ve learned to get up, get moving, go for a slow walk and then start running, it works every time. Another example, I often run 3-4 miles and then lift moderate weights. I’ve often woke up feeling the same way as above, took a walk, felt good enough to run, then started lifting, telling myself I was only going to “go light” (say 3 sets of 8) and, after the 2nd set, found I had the energy and ability to do a full five sets of 8 etc.
Bottom line, listen to your body BUT, be wiling to push it a little bit too. Make sure you get your electrolytes (keto aide rules!) and take some supplements if you are used to them (I use zinc, mag, fish oil, vitamin D, potassium etc…) and, Phiney and Volek suggest sodium 30 minutes prior to a workout and a warm up period.
Good luck in your efforts. The great thing about being a fat adapted runner is you can hit the road without worrying about carrying calories with you and/or go for a run even though you haven’t eaten in a few days, it’s very liberating.