It sounds like things are going well, all things considered. Rather than being in a party house, she's opted to stay with a family that will protect her. This is truly good. How long she'll last there is another question.
No matter, we all have to live with our own moral code and act accordingly. I would not be thrilled if my daughter would live with a boy but I wouldn't be particularly upset if it was someone she had been seeing awhile and someone who had a decent work ethic and values and, of course, treated her well. But that's me.
I do agree you should not lie to the boyfriend's parent. I wouldn't volunteer the information but I would certainly tell the truth if asked. Hopefully, he will tell them himself. As for your daughter, it sounds like she is honest with you -- at least as honest as an 18 YO can be. (I'm not convinced that teens, especially immature ones, really can be 100% honest -- partly because they have to test the waters and partly to see what they can get away with. The majority get over this trait and become the type of adults we hope for. Some don't and always seek the easy way out. My gut feeling is your daughter will be in the majority.)
As strange as this sounds, you may not approve of what your daughter is doing but you can be proud that her basic choices have not been that bad -- no moving into a party house, still going to school, going to where she will be protected and helped. Even more importantly, be proud of the way you are handling all of this -- from the unemotional response to her news of where she was staying to detaching enough to make things more comfortable for your kids at home. You're doing great!