Hello,
Since the anvil process has to run continuously (and this is new in Dovecot 2.2 which was bundled with cPanel 11.40), the process will never end (it's not supposed to), unless dovecot is restarted. That being said, it means that csf/lfd will report this as a process that is running for long periods of time. The solution posted earlier, is the official solution from csf/lfd support to fix this issue.
The anvil process running all the time is NOT a bug or error, it's supposed to run all the time.
The warnings you get from lfd are simply standard default when a process runs for longer than 1800 seconds (default). And csf/lfd combat that by adding those processes that run for long periods of time to the csf.pignore file.
So to reiterate, add the lines to the csf.pignore file as stated (there are others already listed there by default for this same reason), and the issue should be resolved.