First off, I am assuming that you mean "before 1968 did US Presidents and/or individual states...".

Yes, individual states did take some action to handle lynching on their own. South Carolina passed an anti-lynching law in 1896. That law penalized counties where lynchings took place financially.

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Although anti-lynching sentiments were prominently expressed as early as Theodore Roosevelt's presidency [Ziglar, William L., "The Decline of Lynching in America," International Social Science Review, Vol. 63, No. 1, Winter 1988, 14-25] lynching began to become a greater national political issue following the increase of lynchings between 1917 and 1919 (some tie the rise in lynchings to the film Birth of a Nation, which was tremendously popular in the American South). The Dyer Anti-Lynching bill introduced in 1918 brought the issue to the greater forefront of media and national consciousness. The legislation was later endorsed by President Warren G. Harding. Opponents of the bill cited states' rights as a reason for their opposition, claiming that the murders that resulted from lynch mobs were already illegal under state law. On the extreme end, opponents like Rep. Fenis Garrett of Tennessee said the legislation would have the impact of legalizing rape (many blacks were lynched for alleged or perceived crimes against women). [Rable, George C., "The South and the Politics of Antilynching Legislation, 1920-1940," Vol. 51, No. 2, May, 1985, pp. 201-220]

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The best description of state-level anti-lynching legislation that goes to your question comes from a 1934 article in the American Bar Journal:

Anti-lynching legislation is broadly of two types. It is punitive or prophylactic, seeking on the one hand to punish when a lynching has occurred?on the other, to anticipate and prevent lynchings. The main types of punishment are: (a) punishing lynchers by making lynching and mob violence statutory crimes; (b) fining counties and cities in which lynchings and mob violence occur; (c) removing delinquent peace officers. Often special procedures are set up to facilitate the infliction of these penalties, such as: prosecution on information in lieu of indictment, prosecution by the State's Attorney General, and provisions for offering rewards and hiring detectives. The most familiar type;s of legislation designed to prevent lynchings by anticipating them are provisions for: (a) employing military force to guard a threatened person; (b) changing the venue of his trial; (c) calling a special term of court to try him, and (d) removing him to the jail of an adjoining county.'

Although lynching and mob violence under the common law have no technical signification, statutes have made lynching a crime, sui generis, in six states -- Alabama, Indiana, Kansas, Kentucky, Virginia and North Carolina. The same is true of mob violence in four states-- Illinois, Pennsylvania, New Jersey, and West Virginia. Four states have pro visions for accessorial liability?Alabama, Indiana, Kansas, and Kentucky. Kentucky provides penal ties for attempted lynching. Where death is a part of the statutory offense the maximum punishments are life imprisonment or death. Where injury only is necessary, the maximum penalties vary from five to fifteen years. [Chadbourn, James H., Lynching and the Law," American Bar Association Journal, Vol. 20, No. 2, Feb. 1934, pp. 71-76]

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Different historians attribute the decline in American lynchings to different factors. Some it to the advent and development of modern capital punishment and the modern death penalty. [Pfeifer, Michael J., Rough Justice: Lynching and American Society, 1874–1947, 2004, University of Illinois Press] Other historians attribute the decline to the large amount of media attention that lynchings received nationwide, and to the increase in anti-lynching advocacy. [Wood, Amy Louise, "The Spectacle of Lynching: Rituals of White Supremacy in the Jim Crow South," American Journal of Economics and Sociology, Vol 77, Nos. 3-4, 2018] Prominent individuals including Eleanor Roosevelt spoke out against lynching as well (although her husband did not advocate for anti-lynching legislation).

The reality is it was a combination of both of these factors, and general changes in society between the world wars.