an African animal

I can't comment on why Chinese culture focuses on lions, but it's worth pointing out that lions once ranged throughout much of Asia as well. Although by now the only Asian lions left are in the Gir forest in India.

Considering their historic range, it's not surprising that they could have a significant influence on a lot of Asian cultures

Not a direct answer to your question, but just to point out that historically, the range of the lion extended across much of the Near East and well into South Asia. See this map.