Object of class Craft\ElementCriteriaModel could not be converted to string
You'll want to use block.icon.first() if you just want the first Asset, or you could loop through all Assets:

{% for block in entry.visitorContentBuilder %}

    {% if block.type == "listItemWithIcon" %}

        &lt;ul&gt;
            {% for icon in block.icon %}
                &lt;li&gt;{{ icon }}
            {% endfor %}
        &lt;/ul&gt;

    {% endif %}

{% endfor %}


See here for a description of the difference between an ElementCriteriaModel and actual fetched elements in Craft.