I've just happened upon an intriguing comparison of the Lochner-era cases, Meyer v. Nebraska (1923) and Pierce v. Society of Sisters (1925) in Rutgers Journal of Law and Religion, published in 2012. The piece, entitled Pope Pius XI's Extraordinary -- But Undeserved-- Praise of the American Supreme Court is authored by David Upham, Director of Legal Studies and Associate Professor in the Politics Department at University of Dallas.
Though Meyer and Pierce are generally cited together for the proposition that the 14th amendment protects the right of parents to direct the upbringing of their children, Upham shows that the manner in which the Court reasons to that right is distinctive in Meyer and Pierce, though they deal with similar questions and were decided within two years of one another. According to Upham, in Meyer, the Court uses expressly natural law reasoning to depict the integral relationship between marriage, procreation, and educational authority: the parent had a "natural duty to give his children education suitable to their station in life..." to which a corresponding "right of control" in the parent was secured by the common law and 14th amendment. Upham argues that, unbeknownst to Pope Pius XI who praised the Court's opinion in Pierce, its authors were actually no friends of natural law theory (whether of the Thomistic or Lochnerean variety).
Note that in Meyer, unlike Pierce, one reads an express statement that the common law and the Constitution served merely to recognize and guarantee, respectively, these natural familial rights, but not to establish or create them....Furthermore, unlike Pierce, which defined parental authority to include even the power to determine the child’s “destiny,” the Meyer opinion indicated that natural (and common law) rights are ordered to a pre-established natural end or destiny; that is, these rights are all essential to the pursuit of happiness.