Varnish works well with CSF and LFD. However, LFD can get quite aggressive and may decide to kill the Varnish process for one reason or the other. It's prudent to whitelist the varnishd process using /etc/csf/csf.pignore file. Here's a line to add to the csf.pignore file:
exe:/usr/local/varnish/sbin/varnishd
Be sure to restart CSF (csf -r).