Actually, and more to this (Lawrence) point, I think it was that a woman's right to privacy trumped the right to life of the unborn, which is obviously idiocy of the first water. And you're right - they had to declare the unborn "non-persons" to get away with it, which is also clearly sophistry.
In Lawrence, however, privacy is raised legitimately. No one's rights are violated by what adult homosexuals do in privacy. This is in stark contrast to Roe, where someone's right to life itself is being violated.
More often than not, homosexual sodomy infringes on their own inalienable rights, which the judges have declared null and void.
You must already understand that homosexuals do not want to legalize sodomy so that they can continue practicing it in the privacy of their homes and closets. They are now jubilant over this ruling because they correctly percieve that they now have a legal weapon with which to try to force same sex marriage, homosexual adoptions and foster parents, openly homosexual teachers, youth counselors, renters, employees, open homosexuals in the military, on the rest of society EVEN IF WE DON'T AGREE. It isn't the slightest about what they do in private. It's about teaching fisting and sodomy in schools, on TV, in private or public organizations. It's about sodomizing society.