Should everyone get the Critical Ring?

Lies. People here said jobs without a passive critical skill should get the cruel ring

In terms of absolute damage whoring where you go for that 0.1 of a percent (1/1000 damage increase) yes the Cruel Ring wins over Lilin's 3rd ring, in some cases (no natural crits, very low skill %, but high base stats - eg. a DrK with 1000 str and 170% crusher might be better off with the Cruel Ring, by that fraction of a percent).

For all practical measures the Critical Ring is more useful, and if you have Lilin's 3rd, you shouldn't bother with the Cruel Ring.