High CPU, Low PLE relationship

If a server is experiencing high cpu (extended periods over 80%) and PLE is consistently between 400 and 800 seconds on a machine with 180GB RAM...
assuming queries are optimized, etc., etc.,
could the low PLE condition be contributing to the high CPU?

High CPU is typically due to missing indexes. Have you checked for high-value missing indexes?

A low PLE like yours is an indication of memory pressure. Memory pressure would mean more disk access. But it also could be a bad query has a high memory grant.

Which version of SQL Server are you using? And which build of it? (SELECT @@VERSION)

Using SQL 2014 CU7

I have read a number of posts and blogs relating to high cpu, and the likely causes. Yes, we have bad queries, missing indexes, etc. But, that was not my question.

I was specifically looking for an answer to my question "could the low PLE condition be contributing to the high CPU?", where the word "contributing" is the key word in my question. If low PLE does not "contribute" to CPU usage, then my question is answered.

I wouldn't call it contributing, I'd call both a symptom of a problem, likely the same problem.