2. Because of its lateness, we went home.
3. Because of its too lateness, we went home.
(Is #2 or #3 grammatical?)
Use only #1 -- 2 and 3 aren't correct, as is.
Yes, sentence #2 is grammatically correct. It uses "because of" instead of "because," but the overall structure and meaning of the sentence remains the same. "Because of" is a preposition that introduces a noun phrase, in this case "its lateness," which functions as the reason for the action of going home. Both sentence #1 and sentence #2 convey the same meaning with slightly different sentence structures.