'catch someone out on sg.'

Hi everybody,

I found this expression with an explanation not so long ago (in learning material) but I didn't find it in a dictionary (Macmillan, Longman, Cambridge, Oxford, Merriam Webster). I found 'catch someone out' (that is possibly the wanted thing). The mentioned example was:

I caught him out on a lie one day, but he denied it when I wanted to discuss it with him.

My questions:

1. Does 'catch someone out on a lie' exist? (If I remember well I also saw it with 'in' instead of 'on' somewhere. More confusion.)

2. How should I know that the appropriate preposition is 'on' if I can't find it in monolingual dictionaries?

By the way, it seems an important expression, so I really would like to know the solutions to these questions.

Thanks for your answer(s) in advance.

One of my other questions (unanswered): http://www.EnglishForward.com/English/AtWeekendsWeekend/bgnbhj/post.htm