Write a service class that handles saving and sending email then rewrite the store method.

CustomerController.php

<?php

namespace App\Http\Controllers;

use App\Http\Requests\CustomerRequest;
use App\Services\CustomerService;

class CustomerController extends Controller
{
    public function store(CustomerRequest $request, CustomerService $service) {
        $service->store($request->name,$request->email);
        return [
            'saved' => true
        ];
    }
}

CustomerService.php

<?php

namespace App\Services;

use DB;
use Mail;
use App\Mail\WelcomeNewCustomer;

class CustomerService {
    public function store($name,$email) {
        $data = array (
            'name' => $name,
            'email' => $email
        );

        DB::table('customers')->insert($data);

        Mail::to($email)->send(new WelcomeNewCustomer($data));
    }
}