It is almost impossible to have live updated solution on WordPress + PHP servers. One day it'll kill your website and server. I've already posted some thoughts for live change here: https://wpforo.com/community/general-discussions/upgrade-suggestions-for-2020/#post-55414
You could try something like Tawk, but in all honesty, the biggest issue with free live chat plugins/software is that their customer support is inefficient, and the lack the features necessary for an incredible and satisfying live chat experience.
Right now I pay $29 a month for chatwee, the software is great but the support is shit!!!!!!!!
The chat makes my site crash and go down, they say they are working on fixing it but havent got back to me for nearly a week now!!
I pay for support, it part of my package, and they dont even get back to you to let you know whats going on!!
Im just gonna hold out until wpforo and gvectors get theirs sorted.