Failed to use SQLite input. [SQLITE_ERROR] SQL error or missing database (no such table: since_table)

I haven't worked with sqllite plugin before but my guess is that Logstash has to have permissions to write to the sqllite database in order to create the since_table.
The source for this is here:

https://github.com/elastic/logstash-contrib/blob/master/lib/logstash/inputs/sqlite.rb

Check your file permissions and maybe allow the logstash user to update the sqllite db file.