There is a total difference as to why men and women lie about the number of sex partner they had. As a woman, once your partner asked, you do not have any option but to say the truth, or lie. But once you say the truth, expect that your partner will either judge you and your sexuality, or will not care at all.
If the first one will occur, this makes a woman think that she is some kind of a sexual object with less dignity, and worse, some kind of dirty. Because, yes, women, since ages, are expected to be like Virgin Mary until the time they are married. Or if not like of a Virgin Mary, at least to have only one bedded man or partner. They basically lie to ensure peace and respect in the relationship.
The kind of personality a man has is also a factor whether a woman will lie or not. If the man is some kind of religious, the woman will totally lie and lower down the number. If the man is rough and like it wild, the woman may also lie and climb the number so she looks interesting in bed.
While men, on the other hand, are not expected to be virgin at all. They can have as many sexual partners as they want giving justice to their macho image. Most of the time, they report extreme numbers rather than giving exact number because it rise up their self-confidence. But when they feel like they had too much sexual partner that their partner may doubt about their sexual health, including infected with HIV or AIDS, they lower the number. They lie because they also want to have peace or harmony, or they want to look real hot before their partners’ eyes.