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var modal = $('#modal');
$(document).ready(function() {
    setTimeout(function(){ 
        lity(modal);
    }, 3000);
});  

<div id="modal" class="modal" tabindex="-1" role="dialog">
    <div class="modal__container" role="document">
        <div class="modal__col">
            <div class="box">
                <h2 class="modal__title font-display-2 text-blue">Welcome to our new site!</h2>
                <button class="modal__button button button--blue">Contact Us</button>
            </div>
        </div>
    </div>
</div>