Many people don’t eat breakfast. If you don’t want to lose weight bump up your caloric intake.
You should be perfectly fine running, your system already has a reserve of glycogen that it can tap. If you are trying to improve on your speed or want to do hills it will have an impact as the more fuel that is readily available the better, but it would not be a show stopper. Lack of nutrients after a hard run also hinders recovery slightly.
Hey bud, check these guys out. They aren’t huge proponents of fasting but this video seems to answer your question. I’d say if you’re lifting 1 x 36/48 hour fast every week or fortnight wouldn’t do you any harm and you’d see some of the fasting health benefits touted while still being able to gain muscle with a smart resistance training program doing this as long as you’re eating slightly over your maintenance calories over the week as a whole (eat more on your eating days maybe aiming for the higher end of the spectrum of grams of protein, say 1g/lb+ of bodyweight as opposed to 1g/lb of lean body mass.
https://www.youtube.com/watch?v=0HLD7SafCsk
TL;DW Both dudes are big and strong and advocate for 1 x 24 hour fast a week sometimes and advise their clients to do it (even competitive bodybuilders) to re-calibrate their relationship with eating.
edit: or just go for the 16/8 or 18/6 every day approach and get enough protein/fat in your window in which case you’d likely be fine with the usual recommendation of 1g protein per lb of lean body mass. From what I’ve read/watched recently the higher protein intake is generally advised for those cutting and trying to preserve muscle mass.
Try full on fasting to cut the fat off. No intense exercise for 2 weeks of water fasting. You will lose more fat than muscle and because you haven’t damaged any muscle with intense exercise, you will maintain similar muscle density. Then. When you acclimate back to eating, you can do your exercise and consume those proteins to repair the damaged muscles so they can grow bigger. You will be leaner than ever basically with the least amount of effort required.