Can authorize method in Request class return customized message for HandlesAuthorization trait?

I believe you shouldn't look at HandlesAuthorization trait. All you need to do is implementing failedAuthorization method in your request class.

In FormRequest class it's defined like this:

/**
 * Handle a failed authorization attempt.
 *
 * @return void
 *
 * @throws \Illuminate\Auth\Access\AuthorizationException
 */
protected function failedAuthorization()
{
    throw new AuthorizationException('This action is unauthorized.');
}

so all you need is to override this method in your UpdateRoleRequest class for example like this:

protected function failedAuthorization()
{
    throw new \Illuminate\Auth\Access\AuthorizationException('User has to be an admin.');
}