Hey @mrbearps,
We have not tested any live chat plugin with Tutor LMS yet. But from my experience, I am suggesting below.
Hire a developer if you do not know how to customize PHP and WordPress code. We have documentation about how to override our files. So, follow that and add a new field on instructor dashboard settings to add the code for the live chat widget.
Then override the lesson and course templates or use a hook from our documentation to add the chat widget for the student. If you use the same vendor, then this will be really easy.
In this way, the chat management feature will be off the site and handled by the instructor on his own.
The one inconvenient thing is that the Instructor will have to sign up for the chat service on his own and get his own dashboard and access different kinds of data and conversation. As an admin, you can not manage everything for the instructors and signup for a service and use it without a huge amount of custom code.
If you want the chatting system inside your site, then you will need to hire a team of developers to implement API level integration with a chat service provider. That would be quite expensive.