In Lear, there is certainly something to be said about the importance of Warrington being tortured.
Warrington is a loyal to Lear. His loyalty, though, proved to be the downfall for him (but not based upon his relationship with Lear). Instead, Warrington was tortured based solely upon the fact that he was loyal to Lear by Bodice and Fontanelle, Lear's daughters.
Given that Bodice and Fontanelle rebel against their father, the point becomes seen that they are willing to hurt him (Lear) in any way possible.
The torture of Warrington also holds some ironic value. Given that Fontanelle first objects to the killing of a workman, it is ironic that she chooses a workman of Lear's to torture. Not only does this provide irony, it shows Fontanelle for who she truly is: a very cruel person (based upon the fact that she becomes excited at Warrington's suffering).
Similar to her sister, Bodice is also cruel. While first objecting to the murder of a workman (like her sister), Bodice's own cruelty is seen as even greater than her sister's based upon the fact that she simply sits and knits during Warrington's torture. She is completely unmoved by it.