Wreck congratulations on your new job!
Totally agree about more trouble for lying than not. We tell DS the same. He is generally very honest though at least that's what KIGa have told us. I like the idea about closing your eyes!
Hales it is tough. I agree wth you. You know she is lying and I don't think it should go unchallenged. Yes she has been through a lot and I know that makes things delicate but she can't and won't be treated that way for her whole life....
Would he accept H telling him porkies? If you can agree on how you deal with H potentially telling porkies can you then use that to agree on how you deal with DSD? Just an idea 

I have brain ache. Spending the week in German, writing, reading speaking and then it's at a "work" level is really good brain exercise it hurts and I'm enjoying it but I am exhausted.
Plus DS has spent the week fighting a nasty virus which means fevers, coughing and mucho wriggling all night. 
But DH has been a star in supporting me and looking after DS to make sure I can go "to school" every day 