“heart of a lion/lion heart” reminds me of the kind---Richard the Lionheart, the its Chinese translation is “狮心王查理”, if without any more detail, the translation could just be "狮子心" “狮心” each one is fine. "spirit of a lion/lion spirit" , it's an concept more abstract than the first one. i will translate it to "狮魂" or "雄狮精神"

I think it's better to give a description of the phrase. It is to describe a group of sport o a name of a movie? Literally, it traslates as“ 狮子之心”，狮子精神“。