In many Disney movies where the main character grows up during the duration of the film, the characters that were adults when they were young don't visibly age a lot of the time. Examples:
Tarzan - After Tarzan, Terk and Tantor have become adults, Kala, Kerchak and the other gorillas haven't visibly aged.
Sleeping Beauty - Aurora and Phillip age, but their parents and the fairies remain the same
The Little Mermaid 2 (
) - Melody grows up yet 12 years later Ariel, Eric, Sebastian and Triton are all still the same (though flounder did get older)
The Hunchback of Notre Dame - Frollo's appearance never changes during the twenty years Quasi lives in the Bell Tower
Treasure Planet - Sarah Hawkins looks the same before and after Jim is older
Bambi - The Great Prince of the Forest always has the same appearance.
The same goes for TLK - obviously the characters have gotten older (Since Simba is very definitely an adult now) but they just haven't changed in appearance to have visibly aged. I personally would have found it very distracting if they had had grey hairs or saggy skin or whatnot.