Intercom has some docs around sending custom events to Intercom at: https://docs.intercom.com/configure-intercom-for-your-product-or-site/customize-intercom-to-be-about-your-users/send-custom-user-attributes-to-intercom

Step 1. Go into Intercom and create a custom attribute as a string. In the example below, we call the custom attribute "lytics_segments". 

Step 2. Make sure this snippet is installed above the Lytics tag:

window.liosetup = window.liosetup || {};
window.liosetup.callback = window.liosetup.callback || [];
window.liosetup.callback.push(function(){ Intercom('update', {"lytics_segments": lio.segmentsString}); })

When lytics data is loaded it is going to send to intercom. You just need to make sure the update field is the same exact name as the intercom custom attribute/field name. This will send a comma separated list of lytics segments to intercom in the lytics_segments attribute.