Lungisa has filed an application to the Constitutional Court for leave to appeal against the sentence, and wants to be freed pending the outcome of the application.
The National Prosecuting Authority (NPA) had said it would oppose bail.
The Herald newspaper reported that Lungisa, a married father of seven children, is petitioning that he is not suited to the unpalatable food, uncomfortable sleeping arrangements, risk of violence and degrading ablution facilities that come with a prison sentence.
His appeal against his two-year sentence was dismissed by the Supreme Court of Appeal (SCA).
The SCA found no basis to interfere with the sentence imposed by the trial court as it found the crime committed by Lungisa was serious and had devastating consequences.
Lungisa's ANC membership has been suspended, in line with the ANC national executive committee's stance that anyone with a conviction should resign for the sake of the party.