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Something that annoys, frustrates, or worries    
And delivered just Lot, vexed with the filthy conversation of the wicked:
The Lord does not pour His wrath on His people.     He delivers us from evil even when He is judging the wicked.     

Lot was considered just precisely because he was vexed by wickedness.     Those who take pleasure in evil and evil doers are not just.

(For that righteous man dwelling among them, in seeing and hearing, vexed his righteous soul from day to day with their unlawful deeds;)
A person In Christ is vexed by unrighteousness.     Not being vexed by wickedness is a sign of not being righteous.