Changing group_type to mailinglist fails with unknown db error / deadlock
This sounds like corrupt tables or a stuck MySQL process.

If you have access to phpMyAdmin, you can select all tables at the bottom and then choose "repair tables".

If you do not have phpMyAdmin, but you have access to ssh then you can use mysqlrepair (or mysqlcheck -r), see more at http://linuxcommand.org/man_pages/mysqlcheck1.html

If you have neither you should ask your hoster to do a repair for all tables.

Besides that, restarting MySQL makes sense.

If you need further MySQL tweaking, please look at http://mysqltuner.com/
Nothing I have seen beats that script.