Hi again,
I found solution and would like to share. It's not a fault of ADO.NET provider. If you have problems with DataSet like above then just download and install:
SQL Server System CLR Types
I found this solution here:
http://www.tech-archive.net/Archive/VisualStudio/microsoft.public.vsnet.ide/2009-02/msg00022.html
Now everything works for me like a charm. Thanks for great SQLite wrapper!
Greetz!