I'm sorry for your situation.
I don't think you have lied to your ds at all, but you haven't told him the whole truth, which is totally understandable. But he may have found out, or worked out his own conclusion. Which may or may not be as bad as the truth. I'm not sure telling him over the issues of schools will resolve it, in fact it may make him more resentful, as though you're emotionally trying to bribe him to agree with you. I would choose your time to tell him, find a good time when he can question you and feel supported.
I do have a story to share:
My dm had a friend who was taken into hospital after finding cancer, to have it removed. Very much a routine operation, they hoped to remove it all and not even need chemo afterwards. Dm saw her son, who was 13yo at the time, and asked him how she was, knowing that the operation was the day before. The conversation went like this:
"and will she be home tomorrow as expected?"
"that's what dad's telling everyone."
"Oh good."
"I won't see her again though. She'll die in hospital."

The thing was, dm found when she talked to him about it, was that they had been bright and breezy "oh it'll all be fine..." and he had decided that they were trying to hide it. He, in turn, had hidden from them that he thought this, and felt he couldn't ask, and talk to them about it because they were telling him it was no issue and not to worry.
So dm had a 13yo boy she didn't know very well in tears in the middle of town with no way (before mobiles) of contacting his parents, and no way of convincing him that what she was not just giving platitudes.
She managed to contact the neighbours to let them know, and took him to the hospital to see his parents. But if she hadn't happened to see him-he was planning on running away that night, he'd got his bag packed, he was going to try and sneak into the hospital (20 miles away)and see her "one last time" and run away for good.
But actually I think you have last say on schools. Children can be taken on one single thing, which actually will effect them very little. I would discuss it, and let him have his say, maybe both write down the good things about each school? But you have the final say. Would it be possible to say to him that you will be happy to review after a year,. and if he's not happy you will move him to the other school? I did that with dd1, and at the end of a year, she didn't want to be moved.
On the pastoral side, you do need to be careful. Try and find people who have experience. One local school has outstanding on Ofsted and sounds impressive on paper. I know from people who have dealt with them that actually when it comes to using it, it is worse than useless. Thie main way of dealing with issues is to swear they aren't an issue-even when evidence is in front of them.
Another school that had a bad reputation generally, it's pastoral side is excellent according to all who use it.
It's very easy for a school to say "we have all this for pastoral problems" but whether they acknowledge things to be a pastoral problem and then use it, is another matter.
Sorry, that's very long.