No they're just both based on Bambi.
This isn't to say I agree with most of the claims of the Lion King jerks offs have. The notion that no one on staff even had a passing awareness of Kimba is insane and disingenuous. One of the main guys responsible for that era was a weeb who lived in Japan for multiple years, The Great Mouse Detective directly lifted it's ending from Cagliostro (I know that scene itself is based on other films, the Great Mouse Detective writers sited Cagliostro specifically) and Ariel is directly based on "Ghibli girls" (Clarisse and Nausicaä). No one on staff having at least a passive knowledge of Kimba existing is insane.