Based on a limited sample of native Russian-speaking friends, I've come to understand that the adverb "абсолютно" used as a sentence-word in a response is synonymous with "no" as in:
-- Неужели Вы врали?
-- Абсолютно!
More recently I've come to doubt that this usage is as widely understood as I thought, and it probably depends on context. I would appreciate some clarification and possibly some linguistic reference similar to this article https://refdb.ru/look/2896246-pall.html which, ironically, deals with a similar problem in English.