"In real life" with no article is the more common expression that you are likely to hear or read anywhere in the English speaking world. (A Google Search of the phrase yields 287,000,000 results contrasted with "in the real life", which only produces 42,000 results.)
The phrase pretty much works the way the phrase "in life" works. In life (in life in general) this happens or that happens. In contrast "in the life" refers to a specific life: In the life of Albert (a specific, particular person).
In real life (in general, real life as opposed to imagined or fictional life), we do this or that.
In the real life of the president (as opposed to the imagined, fictional, or publicly viewable life), he does this or that...
The phrase can also be used as an adjective to describe something:
In real life stories about .... (general)
In a real life story about .... (specific)
In the real life story about ... (specific)