OOC:
Well, in all likelihood, it wouldn't closed off
forever. However, you would have no way to get back. And without a full magic-user, you're not likely to be able to figure any alternatives out. And even if you did, you probably don't want to take the time.
The way the doors work is pretty straightforward, so you should be able to figure out how to get where Stee came from. You should also be able to figure out how to get back to the lake. But if you get back to the lake, you have a big group of morlocks to deal with. You have a huge clue as to which door leads to where the morlocks came from, but no idea which cycle it needs.
As for the goat, I have no problem with it. I make no promises on how long the poor thing will live, but I think taking it with you is freaking awesome and I am totally on board with it. Just don't expect it to be very useful, and it'll have to be protected during combat. However, if you come up with clever ideas for it, I will definitely work with that. If you describe how you try to train it, it could become somewhat useful. Honestly, I love the idea of a pet, and you seem to be very realistic on how little use it will be. And while enemies will behave consistently with their natures (so a feathered lizard will see it as an easy target for dinner), I will in no way be targeting it or anything like that.