You have to add writing rights to the directory in which your sqlite database is stored. So running chmod -R u+w /srv/mysite/ should help.
If a server is using custom user (e.g. www-data) to access the database, the solution could be to change the owner of your database:
chown www-data:www-data /srv/mysite
chown www-data:www-data /srv/mysite/DATABASE.sqlite