I take a pic of Simba or Nala when it's easy to color and create a different character from it.
I'm also an artist. this is one of my pics of Kiara's 2 cubs.
Although, that pic must be one of @Kovu_Oat's art, he creates pics like that.
First, familiarise yourself with how to draw the official characters from the movie. Do lots of sketches of them in various poses and with many expressions. Just get used to drawing in that style. You might want to start by copying stills from the movie, but don't be afraid to use your imagination too.
While drawing the official characters, think about the similarities they have. Do all their eyes look the same? How about the shapes of their mouths? Compare the mane styles on the male lions. Look at how their facial structures vary. You might want to think about fur patterns and colours too. Some of the lions have dark markings on their ear rims and others don't.
The most important thing to consider when creating your own character is that it has not been done before. You don't want to spend hours upon hours working on a supposedly unique character and then realise that they are a carbon copy of someone already in the movie!
Avoid simply recolouring an existing character, but if your character is supposed to be related to someone, they can be inspiration for your own character's look and personality. The most common fan characters I see are Kiara and Kovu's offspring, but that doesn't mean you should take a picture of Kovu and colour him like Kiara! Simba is not a clone of Mufasa or Sarabi, but he has similarities with both. Likewise, Nala and Sarafina have different face shapes.
I decide to design my own cub for Kiara and Kovu. I give her Kiara's head shape, but add extra fluff on her cheeks like Kovu had when he was young. I find inspiration in other family members of the cub too; I give her Simba's mouth shape and jawline, an outlander nose, Nala's eye shape but Kiara's eye distance, and Simba's ear markings. When colouring the character, I go for a colour in between Kiara and Nala's fur, but I make it darker, inspired by Kovu.
Characters that have no relation to any official character can be really creative, but sometimes end up looking like they don't fit in. It's a gamble but it can be very fun.
Sorry for the wordiness, but I hope this helps! :)