I would like to programmatically manipulate the DSDB database.
What do you mean by that? What would you like to do? Maybe you have noticed the Lua scripting. There is a documentation what you can do with it: http://doorscope.ch/DoorScopeLuaAPIDocumentation.html
The API is suited for export and reporting purpose.
Is there a possibility to export to sqlite?
DSDB is Sqlite, but only the backend. If you want to store the data in a relational DB, you have to take care of this yourself; the Lua API (see above) can be used for this. DSDB itself is an object database which I can directly use in the C++ code without translating to and from SQL.