While threadsafe is the default under windows, It has to be explicitly enabled under unix/linux (as I painfully discovered a while ago when I corrupted a database )
You'll have to check if the option is enabled in the source deb.
If it isn't, no wonder it doesn't work. if it is you can still experience locking problems if various thread try to update the database at once, not really different than having separate processes accessing the same database file, so you should be prepared to manage the case even if you're not programming a multithreaded application (it's just a matter of checking the error code and retrying and/or install a busy handler).
It's all explained in the sqlite documentation.