Due to limitations of IE11 all your contact widget codes, (contact forms, chat buttons, invitation codes) has to be added to your website with fixed protocol. So instead of the default version of button code without protocol like this one:
<script type="text/javascript">
(function(d, src, c) { var t=d.scripts[d.scripts.length - 1],s=d.createElement('script');s.id='la_x2s6df8d';s.async=true;s.src=src;s.onload=s.onreadystatechange=function(){var rs=this.readyState;if(rs&&(rs!='complete')&&(rs!='loaded')){return;}c(this);};t.parentElement.insertBefore(s,t.nextSibling);})(document,
'//yourdomain.tld/LA/scripts/track.js',
function(e){ LiveAgent.createButton('ae94d40c', e); });
</script>
you must add the code with a fixed protocol. If your LiveAgent installation has SSL certificate installed and works via HTTPS then feel free to add HTTPS: and if not then add only HTTP:. However please keep in mind that button/widget with HTTP will not work on SSL secured websites loaded via HTTPS.
<script type="text/javascript">
(function(d, src, c) { var t=d.scripts[d.scripts.length - 1],s=d.createElement('script');s.id='la_x2s6df8d';s.async=true;s.src=src;s.onload=s.onreadystatechange=function(){var rs=this.readyState;if(rs&&(rs!='complete')&&(rs!='loaded')){return;}c(this);};t.parentElement.insertBefore(s,t.nextSibling);})(document,
'https://yourdomain.tld/LA/scripts/track.js',
function(e){ LiveAgent.createButton('ae94d40c', e); });
</script>
