Lucius picked Ginny to discredit Arthur who was trying to get a "Muggle Protection Bill" passed by the Wizemagot. He thought when it came out that Arthur's daughter had opened the Chamber and been behind the attacks on Muggleborns, it would make Arthur a hypocrite and his Bill would be voted down.
Voldemort had nothing to do with it. As the poster above pointed out, Lucius thought Voldemort dead, he only knew that the influence of the Diary would open the Chamber. He had no idea it was a Horcrux.