Let say you want to receive a sms message then users request a chat. Or just send chat data to some external service. This is very easy archievable just using extension. For example I suggest to have a look at https://github.com/LiveHelperChat/livehelperchat-extensions/tree/master/sevabot

It uses one live helper chat provided events

• chat.chat_started - https://github.com/LiveHelperChat/livehelperchat-extensions/blob/master/sevabot/bootstrap/bootstrap.php#L14

This event is fired then user starts a chat from chat widget, standard chat window or from read operator message.

Also chat has antoher even which you can use then chat is closed 

• chat.close - https://github.com/LiveHelperChat/livehelperchat/blob/master/lhc_web/lib/core/lhchat/lhchat.php#L1024

This even you can use then chat is closed and you want to pass some information to third party service.