I wrote about this before in the context of England. I can't speak to the Danish example specifically, but lions were creatures that have been symbols of royalty in heraldry throughout the Middle Ages, and they were kept in royal menageries -- some skulls found in the moat at the Tower of London date back to the 12th century. They were also featured in art; there are lions in the Bible (most famously possibly in the book of Daniel, but elsewhere too) and would have been a creature people were familiar with, even if they hadn't seen them in real life.

In addition to the wonderful answers above (I didn't even think of the biblical connection, but that makes so much sense) , the Barbary Lion would have likely been fairly well-known as it's range is believed to have extended well into the Mediterranean in addition to north African areas that would have been known to Europeans (IIRC the skulls found in the Tower of London were Barbary lions). There are some surviving Greek writings that lament how the lion seems to be vanishing from Greece and Macedonia (Themistius, I believe?) into the first few centuries CE. They were also popular imports for the ancient Roman Bestarii bloodsports, so written accounts of them would certainly not be unknown. This ties into a number of martyrdom stories of early Christians being "thrown to the lions" that remain widespread today.

Lions also were fairly common in medieval bestiaries (albeit not necessarily with a great deal of accuracy), which while not available to everyone still would have been fairly well-known among the educated.

Recommended for more reading:

Blood in the Arena: The Spectacle of Roman Power by Alison Futrell (SUPER interesting read in general)

The Medieval Bestiary - a website that has wonderful sources for further reading and a selection of digitized bestiaries.