The necessary disclaimer: Even today, lions are not a subsaharian species, as there are still wild lions in the Gir forest of India, and they only began to disappear from North Africa and the Middle East in the 19th century, being present in Morocco until the 1920s and Iran until the 1940s. For the Medieval Europeans, the lion might not be on European soil, but it was literally next door, and people were familiar with it.

The Medieval imagery of the lion is largely a holdover of the Roman image of the lion, that is, a symbol of power. You want to appear powerful, you kill or tame lions. You want to show off your power before the neighbor, you keep as many lion pelts around or tamed lions in your menagerie. You want to show your gratitude to some other ruler and adknowledge his status, you gift a lion to him. You want to make your literary character a badass, you write him killing a lion with no effort, or better, you have the lion refuse to fight and 'surrender' to him (see the lion in the epic of El Cid).

But the Medieval imagery of the lion also represented an evolution over the classical past and introduced its own ideas, now passed through the prism of Christianity and the biblical accounts. In addition to being powerful, fierce and strong, the lion also became brave, gallant and wise. Basically, anything a Medieval ruler should strive to be - and the lion in turn became the stereotypical king of the beasts. A rather unique case when it comes to Medieval depictions of predators, who tend to be protrayed as wicked and evil.

Now, each specific lion banner and insignia probably has its own story, but the groundwork is there. Lions are cool. To be called a lion is cool. Why would anyone not want to adopt the lion as their symbol?

What's the usual mod spiel: don't want to discourage further discussion, here are links to previous discussions on the topic, some of them are archived so you won't be able to reply there but you can always reply here?

There's an entire section in the FAQ: Lions in European heraldry

A search for

heraldry lions

limited to this group may provide later hits or hits not in the FAQ.

I skimmed the FAQ articles. You, like many others, mentioned lions being once native to Europe and parts adjacent. But I don't think that was a factor: there were plenty of native fauna and flora that never or rarely made it into heraldry.

I find much more convincing that lions were important animals in the Bible (many references in both testaments: Lion of Judah, Daniel in the lions' den, the Lion of Saint Mark taken from the four animals around the throne of God in Apocalypse), from Greek mythology (Hercules), and with the Romans. And it's not like they couldn't be familiar with the actual beasts, as lions were kept at the Tower of London in England over hundreds of years: Barbary lions were part of medieval Tower of London zoo