No, you can write the entire list without any </li> tags and it's perfectly fine. You also generally don't need to close your <p> tags to start a new paragraph, because paragraphs don't nest inside each other.

This is a perfectly valid html5 document:

  <!doctype html>
  <title></title>
  <ul>
    <li>item1
    <li>item2
  </ul>