How do i fit those eyes into my character mesh? I've created a mesh that doesn't work with round eyes, i tried using the lattice method to make the pupil rotates without moving the eye mesh, but it doesn't worked, even with this modifier the mesh behind the pupil someties moves out of the face mesh. I tried using the vertex thing at the lattice modifier to try to attach the mesh to the eyeballs, but it messed up the model, and didn't attached.
Is there a way to fit a eye into this kind of mesh? here is the file for download: https://www.mediafire.com/file/bdycrc8hqrfajlb/File.blend/file
Both your eye globe and your eye hole have irregular shape, so if you want to solve your problem you need to make them both as regular as possible.
Another way to create your eye would be not to move the eye itself, but to move the texture on the surface of the eye, using an empty as Texture Coordinate Object, like this:

Here is the material setup:

You could get a similar result with the UV Warp modifier as suggested by Lemon.