Yes, it is. Set all the vhost including the catch all vhost (Default virtual host) to disable access logging (vhosts -> log -> access log -> disabled).
In Litespeed admin console (cpanel-> plugin-> LiteSpeed Web Server -> Admin Web Console), under Configuration menu, there should be 4 items: Server, Listeners, Virtual Hosts, Virtual Host Templates. Virtual Hosts is the one to look at.
#Virtual Hosts (0), and there aren't options to select.
Server is using apache config, Actions home page show 5 sites under Virtual Hosts table, but there are no sites/options under Configuration, Virtual hosts.
Then your request becomes how to disable access logging in Apache via cPanel since LSWS gets everything from Apache config in this case. This is not a LSWS issue at all. You may check with cPanel support on how to do that.
You can set LiteSpeed server level log file to /dev/null.
We will change LiteSpeed to stop logging under lsws/logs directory for vhosts configured through Apache httpd.conf