The set for building an app using LitElement, considering IE.

index.html

  <script type="text/javascript">
    // Write me in the head tag.
    // For this sample, you need to put `@webcomponents/webcomponentsjs/` dirctory from the node_modules into `your-doc-root/js/` dirctory.
    (function() {
      if (('customElements' in window)) {
        document.write('<script defer type="text/javascript" src="/js/main.js"><\/script>');
      } else {
        document.write('<script defer type="text/javascript" src="/js/@webcomponents/webcomponentsjs/webcomponents-loader.js"><\/script>');
        window.WebComponents = window.WebComponents || {};
        window.WebComponents.root = '/js/@webcomponents/webcomponentsjs/';

        window.addEventListener('WebComponentsReady', function() {
          window.WebComponents.waitFor(function() {
            var adaptor = document.createElement('script');
            adaptor.src = '/js/@webcomponents/webcomponentsjs/custom-elements-es5-adapter.js';
            adaptor.defer = true;
            document.head.appendChild(adaptor);

            var s = document.createElement('script');
            s.src = '/js/main-ie.js';
            s.defer = true;
            document.head.insertBefore(s, adaptor.nextSibling);
          });
        });
      }
    })();
  </script>

package.json

{
  "name": "sample-app",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "scripts": {
    "test": "echo \"Error: no test specified\" && exit 1",
    "build": "webpack --mode=development",
    "watch": "webpack --watch --mode=development",
    "package": "webpack --mode=production"
  },
  "keywords": [],
  "author": "",
  "license": "ISC",
  "devDependencies": {
    "@typescript-eslint/parser": "^2.10.0",
    "@webcomponents/webcomponentsjs": "^2.4.1",
    "core-js": "^3.4.7",
    "eslint": "^6.7.2",
    "install": "^0.13.0",
    "lit-element": "^2.2.1",
    "npm": "^6.14.2",
    "ts-loader": "^6.2.1",
    "tslint": "^5.20.1",
    "typescript": "^3.7.3",
    "webpack": "^4.41.1",
    "webpack-cli": "^3.3.9",
    "whatwg-fetch": "^3.0.0"
  },
  "dependencies": {
    "@webcomponents/template": "^1.4.1"
  }
}

tsconfig.ie.json

{
  "compilerOptions": {
    "sourceMap": true,
    "target": "es2017",
    "module": "es2015",
    "lib": [
        "dom",
        "es2015",
        "es2017",
        "es5",
        "es6"
    ],
    "moduleResolution": "node",
    "allowSyntheticDefaultImports": true,
    "allowJs": true,
    "experimentalDecorators": true,
    "typeRoots": ["node_modules/@types", "types"]
  }
}

tsconfig.json

{
  "compilerOptions": {
    "sourceMap": true,
    "target": "es2017",
    "module": "es2015",
    "moduleResolution": "node",
    "allowSyntheticDefaultImports": true,
    "allowJs": true,
    "experimentalDecorators": true,
    "typeRoots": ["node_modules/@types", "types"]
  }
}

webpack.config.js

const path = require('path');

module.exports = [
  {
    entry: [
      path.join(__dirname, 'src', 'index.ts'),
    ],
    output: {
      filename: 'main-ie.js',
      path: path.join(__dirname, 'dist'),
    },
    resolve: {
      extensions: ['.ts'],
    },
    module: {
      rules: [
        {
          test: /\.(js|ts)$/,
          exclude: /node_modules\/(?!(lit-html|lit-element))\//,
          use: [
            {
              loader: 'ts-loader',
              options: {
                configFile: 'tsconfig.ie.json'
              }
            },
          ]
        },
      ],
    },
  },
  {
    entry: [
      path.join(__dirname, 'src', 'index.ts'),
    ],
    output: {
      filename: 'main.js',
      path: path.join(__dirname, 'dist'),
    },
    resolve: {
      extensions: ['.ts'],
    },
    module: {
      rules: [
        {
          test: /\.ts$/,
          loader: 'ts-loader',
          options: {
            configFile: 'tsconfig.json'
          }
        },
      ],
    },
  },
];