How to use multiple different instances Element API "Load More" button?
You could add a new param to the request called skip and use that on your homepage, and default it to zero to allow you to reuse the endpoint elsewhere.
$skipEntries = Craft::$app-&gt;request-&gt;getParam('skip') ?? 0;
$criteria = [
    'section' =&gt; $settings['section'], 
    'limit' =&gt;  $settings['limit'],
    'offset' =&gt;  ($settings['limit'] * Craft::$app-&gt;request-&gt;getParam('offset')) + $skipEntries,
    'order' =&gt; $settings['orderBy'],
];

You'll need to add the skip parameter to the data object in the jQuery $.ajax request options object for your homepage implementation:
$.ajax({
    // some params here
    data: {
        skip: 6,
        offset: lazy_offset,
        settings: lazy_settings,
    },
    // some more params here
}

Other pages would omit the skip parameter. That's one way of solving the problem.