Thanks Oliver for pointing out this problem. I actually don't myself use a single Connection in parallel (if in parallel, I use multiple Connections), but the library should support this. The problem comes not from the single Connection, but from the preprepared SQL Statements for attribute access. They are preprepared for speed, but this means one needs to serialise use of the Statement.
I've been burned by Semaphores in the past and won't use them, but I'll use some other method.
Issue: https://bitbucket.org/drjdpowell/sqlite-labview/issues/10/attribute-parallel-access-bug