Hi Zahra,
When a man asks if you live alone, he may be fishing to see whether you are single.
If you were having lunch with this guy, he may already have a degree of romantic interest in you.
Asking whether you live alone may have been an attempt to discern whether you were single without being too obvious about his intent.
He may want to ensure that if he decides to pursue you with romantic intentions in mind, there would be no boyfriend or husband to worry about.