You can do what you are trying to do – add a CSS class selector to an HTML div tag, but you are mixing HTML and PHP code incorrectly. In order to do this correctly, you need to use the PHP opening/closing tags accordingly, such as:
?>
<div class="col-lg-12">
<?php
echo paginate_links( array(
'total' => $total_pages,
'current' => $current_page,
) );
?>
</div>
<?php
Alternatively, you could also do it like this (no need for the PHP opening/closing tags):
echo '<div class="col-lg-12">';
echo paginate_links( array(
'total' => $total_pages,
'current' => $current_page,
) );
echo '</div>';