Oh boy, this is one of those super innocuous questions that opens an absolute can of worms.

Why was Gustavus Adolphus called Der Löwe aus Mitternacht? As far as I'm aware the earliest mentions of this come from pro-Swedish propaganda leaflets printed in 1630 after the Swedish army had landed in Northern Germany but why this specific phrase? This is where things get murky and complicated. It involves prophecies, possibly old ones but also drawing on folklore and heraldry.

So, a lion coming to judge the sinful and create a new land for the faithful is a biblical narrative, found in the books of Isaiah, Daniel and Jeremiah. So, connecting to this biblical narrative was easy for propagandists, the figurative "Whore of Babylon" is the catholic church, Gustavus is the lion coming to judge and and create a new land for the faithful (the protestants). However, there is more than that. The arrival of Gustavus Adolphus coincided roughly with a renewed interest in the prophecies of Parcelsus, primarily by the Rosicrucians and here we find an interesting passage:

"...mighty lion born of northern star will conquer the realm of evil, usurp the eagle's sceptre..."

Does it sound familiar? This tied in neatly with the biblical narrative of a lion sent by god to pass judgement on the wicked. I've encountered various explanations of why "Mitternacht" was chosen rather than "North", ranging from the position of the sun to the direction to the dials of a watching pointing "up" at midnight or even Sweden being the "land of the midnight sun". Another explanation I've encountered is that it was tied to an apocalyptic biblical narrative, the lion arriving at the final hour (midnight). To my knowledge no scholary concensus exists on the topic.

In either case, it is worth bearing in mind that this was propaganda even when it was written and thus likely cherry picked to suit the authors narrative and paint Gustavus as a protestant saviour.