鳴らなくて

[deathelysium]

I don't really understand how is it conjugated...

First: 鳴る
Second: 鳴らない
Then: ???

:@:@

[battousai]

First: 鳴る - dictionary form, to ring
Second: 鳴らない - informal negative form
Then: 鳴らなくて - informal negative te form, as in connective or command form formed by changing the い to くて like you would an i adjective.

[deathelysium]

oh really? I didnt know about the "informal negative te form" :D

[Kates]

I'm guessing it's probably being used with "mo ii desu"... Naranakute-mo-ii desu = You don't have to ring / It's okay not to ring.

This is one way to say 'you don't have to ---' in Japanese.
Tabenakute mo ii desu = You don't have to eat
Yomanakute mo ii desu = You don't have to read ...etc.