As a partial answer, concerning the lying part, it may be adduced that it is permitted to lie from Rema (resp. §2) who permitted a woman to have contact with her husband despite her telling inquirers, early on in her pregnancy, in order to be shielded from the evil eye that she wore clothing designated for her menstruation period because she was unclean and indeed said she was unclean. He does not mention the (non)issue of her lying. This ruling was also brought by Shach (YD 185:5) and likewise did not raise the issue of lying.
R. Shimon Hirari (resp. Lev Simchah, EH §12) justified a woman's white lie, which she told people that she had a ruach (I can't determine if she meant a spirit or bloated), by demonstrating that pregnancy can be referred to as ruach.
However, in both cases it should be noted the woman did not explicitly lie by saying she is not pregnant but rather gave "alternative facts".