She wanted an abortion at the time, but could not obtain one legally in the time it took to have the case adjudicated, and gave birth instead. So she didn't lie in court and neither did her lawyer; the whole basis of her suit was that she wanted an abortion and could not obtain one. I believe she put the baby up for adoption. If abortion had been legal, she would have had one. No one forced her to be a plaintiff; it's not like her lawyer held a gun to her head and forced her to sign the affidavits she did. No matter what she says now, at the time she was perfectly willing to be a a plaintiff through the district court, appeals court, and Supreme Court proceedings. Revisionist history is a great thing, isn't it?
One of the legal issues the court had to deal with was whether her claim was mooted out because she had the baby before the Supreme Court heard her case. If the injury a plaintiff claims is past and cannot be remedied, then the court does not have jurisdiction to hear the case. However, the Supreme Court found that the facts fell into one of the exceptions to the mootness doctrine, namely the "capable of repetition yet evading review" exception. In other words, she could have gotten pregnant again, wanted an abortion, been denied a legal abortion, filed suit, and it wouldn't get heard to finality before the 38 weeks of pregnancy had elapsed. Therefore, her claim was not moot, and the court had jurisdiction to hear it.