Lilies are associated with Easter (this is when they will naturally flower) as it is said that lilies sprang up at the point where Christ's blood fell to the ground from the cross.
It also is said that lilies that are rotting smell like death - hence the allusion to this in one of Shakespeare's sonnets "Lilies that fester smell far worse then weeds"
Folklore has it that lilies will spontaneously grow on the graves of a person who was executed for a crime they did not commit
Throughout history lilies have been associated with chastity, virtue and innocence - the dead were garlanded with lilies in order to pass on some of that virtue to the deceased in order that they might pass into heaven.
The nickname 'Death' lilly was coined after a 17th century chimpanzee experiment went teribbly wrong. The chimp's female matriarch, Lilly, was kidnapped by a Spanish pirate called Wango Jevado and was trained to kill small shrubs...
While Rekstout may be correct as regards lilies in general, the specific type of lily called the "Death Lily" is poisonous, and presumably gets its name from that fact.