The most thing I am missing since years on Livezilla is the modern designed Chat Window for customers. It is possible to change several things but it is still not up to date.
Design from Kayako or Intercom are some nice samples where customer get a gusto to contact you. For Online Shops is that another nice feature to support customer immediatly instead to get a ticket.
Kayako: https://www.kayako.com
Intercom: https://www.intercom.com