reference: https://github.com/yyx990803/laravel-vue-cli-3

Vue CLI inside Laravel

lite version

Nuxt inside Laravel

basically, generate nuxt static dist into laravel and serve the dist like another public folder.

// frontend/package.json

{
  "scripts": {
    // ...

    "pregenerate:laravel": "rm -rf node_modules/.cache .nuxt dist ../backend/dist",
    "generate:laravel": "BASE_URL=/ BASE_DIR=/prefix/ PUBLIC_PATH=/ nuxt generate",
    "postgenerate:laravel": "mv -fv dist ../backend/dist"
  }
}

// frontend/nuxt.config.js

export default {
  // ...

  axios: {
    baseURL: process.env.BASE_URL || '/',
  },
  router: {
    base: process.env.BASE_DIR || '/',
  },
  build: {
    publicPath: process.env.PUBLIC_PATH || '/_nuxt/',
  },
  generate: {
    fallback: true,
  },

  // ...
};

// backend/routes/web.php

// ...

Route::get('/', 'HomeController@serveStatic');
Route::fallback('HomeController@serveStatic');

// backend/app/Http/Controllers/HomeController.php

use Illuminate\Http\Testing\MimeType;

// ...

class HomeController extends Controller
{
    public function serveStatic(Request $request)
    {
        $base = 'prefix'; // or ''
        $dist = 'dist';

        $path = base_path(($base ? $dist : "$dist/") . str_replace($base, '', $request->path()));
        $path = is_dir($path) ? "$path/index.html" : $path;

        return file_exists($path) ? response()->file($path, ['Content-Type' => MimeType::from($path)]) : abort(404);
    }
}

may reference: https://github.com/cretueusebiu/laravel-nuxt