How to break the wp_link_pages in two lines

You could potentially use the before, after, and separator arguments passed to wp_link_pages() to wrap each item in a span, then target the spans via CSS.

Here’s your current code:

wp_link_pages(
    'before=LQ &pagelink=Chapter %'
);

Converting to an array, because it’s easier to follow/manipulate:

wp_link_pages( array( 
    'before' => 'LQ ',
    'pagelink' => 'Chapter %'
) );

Let’s modify it:

wp_link_pages( array( 
    'before' => '<p class="link-pages">LQ<span class="page-link">',
    'after' => '</span></p>',
    'separator' => '</span><span>',
    'pagelink' => 'Chapter %'
) );

This will produce output like (line breaks added for readability):

<p class="link-pages">
    LQ
    <span class="page-link">Chapter 1</span>
    <span class="page-link">Chapter 2</span>
    <span class="page-link">Chapter 3</span>
    <span class="page-link">Chapter 4</span>
</p>

Then you can use CSS to style the <span>s according to your needs.

Edit

Alternative/related suggestion:

You can pass 'echo' => false to return the markup as a string:

$page_links = wp_link_pages( array( 
    'before' => '<p class="link-pages">LQ<span class="page-link">',
    'after' => '</span></p>',
    'separator' => '</span><span>',
    'pagelink' => 'Chapter %',
    // Return, don't echo
    'echo' => false
) );

Then, you can use whatever tools at your disposal (PHP, RegEx, etc.) to manipulate $page_links however necessary to suit your needs.

Note

Please note: CSS and PHP/RegEx are off-topic for WPSE.