when do you feel like you've really lived in a place?

To me a month doesn't count. In my experience it already takes about 2 months to really settle in somewhere.
Some places grow on you faster than others. Once you start making friends, get a regular routine and hang-outs I think that qualifies as feeling "at home". Once you start living a day-to-day life and you are no longer constantly reminded that you're in a foreign country. Once foreign has become familiar.

I agree with globetrotter, a few months is clearly not enough to qualify as having 'lived' in a country. I'd personally say that "I stayed in.... OR I worked in....." if the period was anything less than one year, after that I think it would depend on how I felt about my time there.

In my own case I have LIVED in Brazil for over eleven years now. I count that 'retroactively' to the day I arrived for a number of reasons. Yes, I came here without any guarantee that I would stay permanently, but fell in love with the country. Eventually I married and put down my roots here. Now I have a Brazilian son and at least half of an extended family (my family all remains in Canada). So now I really belong here, I feel like I was born here.

Cheers,
William James Woodward - Brazil Animator, Expat-blog Team

I think you have to live somewhere at least 6 months or a year.  Anything less and you're just visiting.

There are a few people here who like to collect flags.  If you look at some of them they have USA-Connecticut, USA-New York, USA-New Jersey.  Crossing state lines has nothing to do with being an expat.