Hello and welcome to LiveChat!
The only automated e-mail sent from LiveChat in that case would be a new ticket notification that you can disable in Settings > Ticket Settings > Email notifications, here’s a screenshot: https://monosnap.com/file/HrGJh3WK93bIPyDXAe3SzbznhVzbnO
However, there may also be a case when your agents have an Auto responder set up on their e-mail and enabled notifications about New Tickets in LiveChat. With such set-up your clients may receive the auto-responder from agents email after creating a ticket in LiveChat. In that case you can disable the notifications sent from LiveChat for each of your Agents. You can do that by editing their profile settings and unticking the option “New Ticket emails”, here’s a screenshot as well: https://monosnap.com/file/H94xV8aTIBpCxgTmHaCR9N1QnnTpse
Hope that helps, but if you have any further questions I’ll gladly answer