How validate unique email out of the user that is updating it in Laravel?

You can tell that to validators:

'email' => 'unique:users,email_address,'.$user->id

Check the docs, in section 'Forcing A Unique Rule To Ignore A Given ID'.

In Request Class you will probably need this validation in PUT or PATCH method where you don't have user then you can simply use this rule

 You have 2 options to do this

1:

 'email' => "unique:users,email,$this->id,id"

OR

2:

 use Illuminate\Validation\Rule; //import Rule class 
'email' => Rule::unique('users')->ignore($this->id); //use it in PUT or PATCH method

$this->id is providing id of the user because $this is object of Request Class and Request also contains user object.

public function rules()
{
    switch ($this->method()) {
        case 'POST':
        {
            return [
                'name' => 'required',
                'email' => 'required|email|unique:users',
                'password' => 'required'
            ];
        }
        case 'PUT':
        case 'PATCH':
        {
            return [
                'name' => 'required',
                'email' => "unique:users,email,$this->id,id",
                                   OR
                //below way will only work in Laravel ^5.5 
                'email' => Rule::unique('users')->ignore($this->id),

               //Sometimes you dont have id in $this object
               //then you can use route method to get object of model 
               //and then get the id or slug whatever you want like below:

              'email' => Rule::unique('users')->ignore($this->route()->user->id),
            ];
        }
        default: break;
    }
}

Hope it will solve the problem while using request class.