I would have assumed this was a joke, if I had not read, some years ago, an article in
Liberty (I think) making the same point; I don't recall who wrote it. But let me point out that the Interstate Commerce Act (1887) and the Sherman Antitrust Act (1890) were each enacted by a Congress for which no woman voted legally, directly or indirectly. It may be that Lott approves of the Sherman Act, but he cannot reasonably deny that it represented growth of government. I maintain that America's course was set, and not in the direction of freedom, well before women's suffrage was significant.
I may be reminded that Wyoming, where women did have the vote, was made a state in 1890. And so it was: eight days after the Sherman Act was signed into law.
IMO, I think the government grew in leaps and bounds during the Wilson administration. I point to several things that occurred on his watch that contributed to the growth of governemnt - amendments 16 through 19. Income taxes, direct voting of Senators, prohibition, and women voting.
Add to that, public educatin was made mandatory, by law, long before women received suffrage.