Logging showed nothing suspicious and problem popped in several places in non deterministic way. I downloaded SQlite provider sources, added some brake points there and tried to reproduce problem. After thorough testing I found severe problem on our side - there was a place where async code was started and not awaited that used Entity Framework context closure that was running out of scope and was about to be disposed. So basically there was a race condition between this async code block and dying EF context. After making this place sane the problem went away completely.

Thank you for your help!