JSFiddle - React, Tailwind, and code Playground

HTML

<script src="//cdnjs.cloudflare.com/ajax/libs/less.js/1.6.1/less.min.js"></script>
<h2 class="header">Заголовок</h2>
<ul class="menu">
    <li class="punkt1">Пункт 1</li>
    <li class="punkt2">Пункт 2
        <ul class="submenu">
            <li>Подпункт 2.1</li>
            <li>Подпункт 2.2</li>
        </ul>
    </li>
    <li class="punkt3">Пункт 3</li>
</ul>

JavaScript

var lists = $('li.punkt1').next();
lists.each(function(index, elem){
    alert(elem.innerHTML);
});