It's too bad, the place has potential. Cool looking old stone construction, but it certainly didn't look that great while stopping in a few weeks back. For what it's worth, an older gentleman who was a longtime GMC member, advised against me staying there. I was already headed to Pico Camp, an idea he approved of.
Not sure if you've ever seen it, but it's not fully enclosed like you're led to believe by it's "lodge" status on the LT. It's opening looks toward the northwest winds (no glass in the large windows w/ no way to close up,) kinda dingy looking inside. Certainly gets it's share of skier/snowboarder visits judging from the graffiti and stickers plastered everywhere. We didn't stay the night, so I can't speak on the mice or roof leaks from experience.
But, many of the LT shelters have mice. Just keep a clean camp and hang your food, you should be fine. Don't leave your TP around, they'll shred it to pieces!!