You can popup your CRM page when Agents are receiving a call in VICIDIAL and pass Lead info using the POST method. if you want to pass custom fields info as well set CF_uses_custom_fields=Y in the URL as well. This setting can be set at the campaign level in the web form field.
Here is a sample on how to pass the parameters including custom fields.
The next step is to set “Get Call Launch” to web-form so that when an agent receives a call CRM page auto popup.