Nested navigation link list, with active items, and child check - https://www.shopify.com/partners/blog/shopify-link-list

nested-navigation-link-list-full-snippet.liquid

<ul class="parent">
{% for link in linklists.main-menu.links %}
<li {% if link.active %}class="active {% if link.child_active %}child-active{% endif %}"{% endif %}><a href="{{ link.url }}">{{ link.title }}</a>
{% if link.links != blank %}
  <ul class="child">
    {% for child_link in link.links %}  
    <li {% if child_link.active %}class="active {% if child_link.child_active %}child-active{% endif %}"{% endif %}><a href= "{{ child_link.url }}">{{ child_link.title }}</a>
    {% if child_link.links != blank %}
      <ul class="grandchild">
      {% for grandchild_link in child_link.links %}  
        <li {% if grandchild_link.active %}class="active {% if grandchild_link.child_active %}child-active{% endif %}"{% endif %}><a href= "{{ grandchild_link.url }}">{{ grandchild_link.title }}</a></li>
      {% endfor %}
      </ul>
    {% endif %}   
    </li>
    {% endfor %}
  </ul> 
{% endif %} 
</li>
{% endfor %}
</ul>