Lampanelli drew criticism for posting a picture of herself and Dunham at the Writers Guild of America awards, calling the Girls star "my n***a".
MailOnline reported an exchange between Dunham and journalist Shayla Pierce, who wrote a blog on the issue for xojane.com and said Dunham's silence "showed her true colours (sic)".
The writer and actress took to Twitter to defend her position, telling Pierce it was not a word she would ever use.
"Its implications are beyond my comprehension. I was made supremely uncomfortable by it," Dunham explained.
"Perhaps I should have addressed it, but the fact is I've learned that twitter debates breed more twitter debates.
"Don't like the idea that my silence read to you as tacit approval. It wasn't.
"But 140 characters will never be enough for the kind of dialogue that will actually help us address issues of race and class."
Dunham added: "My personal criteria for engaging twitter debate: I wait until something just sits so wrong in my belly & bones that I must finally speak."
Pierce thanked Dunham for her response, adding: "I do [love] you and your work. Thanks for addressing this *hugsies*."
All but Dunham's final tweet have now been deleted from her account.
Dunham recently responded to criticism from Kareem Abdul-Jabbar over Girls's inclusion of "people of colour, sexual preference or gender".