Multiple connections to SQLite with simultaneous async Tasks

In my scenario it has Sync_Class that syncs, with AsyncTasks in background , from my app to my server. Every time that my app does one action that need to change data from my SQLite, as first step my app updates my local database as second step throws a AsyncTask in background to start the sync with my server. In the 80% of cases my app works great but the other 20% of cases throws a IllegalStateException because the app try to re-open the connection or open a closed connection, when I have a method to open database in 6 lines more above. In this cases I think the problem is multiple simultaneous acceses in database, I'm right?

In the differents posts that I can read, the people talk about de SQLite can't execute a simultaneous connections and it serialized connections because file structures not permit... The final question is, If we do multiples asyncTasks with sqlite connections to do inserts, updates and deletes, to harness the full power of the processor with parallel programming, we have any tools for do this? Or it's a non-viable option and we need to do a serialized connections?

If you have any solutions or any ideas for my problem, help me!! Thanks in advance!! If you need more information or something let me know.