Wow. I'm not really sure what you should do, I'll think about ideas today.
One thought would be to give each kid a key-locking doorknob that you/DH have a key to, and so do they, but no one else in the family... But not to SS11, with the explanation of that he can't respect other people's privacy, so hasn't earned his own, and that it's too bad that the other kids can't trust him and have to have locks on their rooms.
I don't know if that's a good idea or not, but it popped into my head.

I just wanted to say that I'll be thinking of you today and wishing you luck with this.

My son is 19 and I have learned that if I tell him to clean his room and if he say 'yeah, okay', it probably isn't going to get done. I have told him (and done it twice) that I will clean it for him. When I clean it, I throw away everything that I don't think is necessary. I told him that means important papers, cords that I don't know what they go to, etc. Now, when I tell him to clean his room or I will, he usually does it. I have had to stand there a couple of times and watch him because he will 'straighten up' and shove things out of sight and call it clean. Nope, I stand there and tell him when it's clean. He's been keeping it clean.

If anyone wants to argue that it's his room or he's 19, blah blah blah, it's MY HOUSE. I don't want to smell his room. I don't want vermin or pests attracted. I want him to learn to be neat so someday, a woman will be able to stand living with him.

(so anyone that has a criticism for me on that.... you do what you want in YOUR house with YOUR kids.)

You need to get on the same page as his mom. All the adults need to speak and communicate and maybe call a pow wow... with him as the guest of honor. Let him know he isn't getting away with anything and that every time he lies, he is letting all of you down and losing his credibility, which he may really want someday. The day may come when he says, 'can I go to the movies with my friend' and he's lied so much, you don't believe he's going to the movies so the answer is no. (or think of other things he asks for...) Turn it around so he can see how he's hurting himself with the lies.

Once, my SD was sick and I made her chicken soup. She didn't want soup and started telling DH how she hated soup. He offered her other kinds of soup and she said she hates all soup. A few days later, we were having Chinese food and when the won ton soup arrived, she didn't get any. She got upset and when she asked why she can't have any, she was told she hates all soup. She had to live with her lie. She has since admitted that she doesn't hate soup and we told her that when she tells us something, we want to believe she's telling the truth and we will hold her to it. If she lies to us, we are not going to believe anything she says. She's gotten better but I think kids just lie to get what they want, when they want sometimes.

I'm still not quite sure what you should do - TBH, I have no idea what we'd do if A__'s exaggerating and occasional fibbing or not telling the whole truth got to that level.
If we think A__ is making something up, we'll ask him some detail like "Really? What's the kid's name who was so bad that he got sent back to grade two and then was so bad that he got sent back to grade one and is now the biggest kid in grade one?" and he realizes he's busted. But A__'s tall tales are nothing like your SS does and that's just not going to be effective for your SS.

Maybe you could try like Pseudo did for her SS's showers? Every time he says he will clean his room, or didn't read his sister's diary, etc, you could make him sign a contract to that effect and each keep a copy. Maybe it could help him feel accountable for his actions and provide you guys with "proof" for him of his past truths and lies.
I know A__ forgets things he said about two seconds after he said them, and can only remember instructions for approximately the same length of time, so having them written down is a HUGE help at our house (ie: I leave a little note on his weekend morning snack that he has to eat it at the table and wash his hands before touching anything else. If we just tell him the night before, but don't leave the note, he "forgets") Maybe your SS isn't remembering what he has done or said and writing it down would help... Also ADHD kids are often very visual and SEEING his promise or actions, in writing, might make it more "real" to him?
My printer is also a scanner and photocopier, so I have photocopied good teacher comments from A__'s homework book, so that if he's down on himself, that can help him remember a good day. Maybe having a written reminder of times that he's told the truth or a lie can help your SS recall how it feels good to tell the truth and feels bad to lie?

I know this may sound lame and like an excuse, but could it be SS doesn't have a clue how to clean up his room? I mean what to do first, what goes where, what needs to be done and what can 'slide', how much is 'good enough'?

I remember having the exact same struggles with my older son (ADHD) and finally, I just got in there aand started cleaning with him. I got him a bunch of baskets for toys and misc. stuff, and aside for using one box for his Lego, he had no clue what to do with the boxes to keep his stuff organized. His only idea for organizing was 'big stuff' and 'little stuff' -- that's it! I finally got some sticky labels and labeled what went where, and that seemed to help. We also used a large tub for things that leave the room -- stuff that belongs elsewhere in the house.

If you decide to go the locked-door route (we did that too), then push-button combination locks are great. Easy to open from the kid's side for fire-safety, but each kid has his own combination. It also assures a few seconds of privacy without having to wait for a 'come in' invitation.

Sweeby, you might have hit the nail on the head. My DD let her closet floor get so cluttered she didnt know what to do. I sat with her, we emptied out the oloset and figured out what to do. She doesnt as good a job as we did togethor, but much better.