命があって良かったって英語でなんて言うの？

"I'm lucky that I survived. " Is saying the the situation was bad and that it was by chance you lived.
"I am glad that I lived!" Here you are saying you are happy to be alive.

"I'm lucky to be alive." This explains to someone that after a dangerous situation you are lucky that you are alive and survived the situation.
Eg: I'm lucky to be alive after that.

"I'm happy to be alive." This explains that you are happy and relieved that you are alive after a dangerous situation.
Eg: I'm happy to be alive after that situation.

To say that you are 'lucky to be alive' is to say that the situation was dangerous and that it was by chance that you survived and lived.

When something dangerous happens and you could be hurt but are ok then you could say 'I'm lucky to be alive' or 'I'm glad I'm still alive'
There is a common saying 'I had a lucky escape' meaning you were lucky to not be hurt

To do something by the skin of one's teeth means that it was only by a very small margin that you were successful. This phrase, which has its origin in the Bible, is usually used when talking about a narrow escape from disaster.