I lost zero noticeable lean muscle mass on my 60 day fast, at least no more than I would have sitting on the couch doing nothing.

There's just not a metabolic pathway for breaking down muscle/organ tissue for energy when you have adequate fat stores. We would have died off as a species a long time ago if that were the case.

In the grand scheme of things, if you have the body fat, 7 days is nothing for a fast.

Edit: To those asking, yes. I fasted for 60 days, water and electrolytes, no calories.