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Being a hero or villain is irrelevant to The Lost Lenore. What matters is that the dead character was important to them, like a Love Interest or The Not-Love Interest, and remains a central influence on the living character long after their death.
Excessive Mourning is a common overlap when they refuse to move on and simply wallow in grief.
Also see the index at Grief Tropes for more ideas.
"You want weapons?! We're in a Library! BOOKS! The best weapons in the universe!" — The Doctor
Love Makes You Evil I think would describe any case where someone becomes a villain out of grief for losing someone they love.
You need to move on
As far as I’m concerned, The Lost Lenore only deals with a villain’s love interest. Is there a more platonic version of The Lost Lenore, where the villain had a family member or really close friend that meant the world to them, and their death is what drove them to villainy. How about if someone is grieving their lost one, and has been doing so for a very long time. The other characters tell them that they need to move on. Is there a trope to describe this?