The important thing to note about the Tuskegee statistics is a racial issue; the United States cannot be cleanly divided between black and white without leaving a substantial proportion of citizens out of the equation. As I do not have access, at least at the moment, to the specific points used by the Tuskegee Institute for those specific years, I cannot say with any degree of certainty whether a Mexican victim would have been placed in white, black, or not counted at all. Likewise for a Chinese or Native American individual, or those who may have been able to 'pass' for a race they were not raised as and who were not identified by name, as happened in numerous cases. If you are interested in sources which perhaps give some greater amount of specificity while still being accessible to the layman and divide lynchings by racial identification of the victim, I recommend this map and this database.

Having said all of that about why I cannot exactly answer your original question, I will attempt to discuss the reasons a white individual (as well as a few of the above-mentioned 'non-black' groups) might have met their death at the hands of a lynch mob during that era. I will define lynching as "violence which leads to the death of at least one individual which is not sanctioned by law and derives its supposed justification from some violation of the social norm; the lynchers are generally in some group outnumbering the victims".

The first group is the easiest to "understand"--abolitionists and civil rights activists such as Elijah Lovejoy (d. 1837) or Goodman and Schwerner (d. 1964), not to ignore James Reeb (d. 1965), a Unitarian Universalist minister who President Johnson named as he gave the draft of the Voting Rights Act to Congress. Then there are the Union soldiers or suspected sympathizers (as in the Great Hanging at Gainesville, 1862), or, later, the Reconstruction Republicans and officials, such as NC State Senator John W. Stephens (d. 1870). And then there are the stories of (relatively) small acts that became a death sentence: William Pierce Mabry (d. 1885) was lynched after defending a black woman from a beating; Ann Derrickson (d. 1863) was beaten during the New York City Draft Riots for attempting to save her mixed-race son from a mob; she later died from her wounds.

Then there are the more, well, straightforwardly racist examples: there are several examples of mass and individual examples of (most often, due to share of the population) Chinese or other Asian immigrants meeting untimely ends, such as the Chinese Massacre of 1871, in which a Los Angeles policeman was wounded, a rancher pursued a Chinese man to his door and was shot for the aggressive behavior, and a white/Mexican mob burned down the Chinatown and killed 17, hanging 14 of them. This event and the 1891 Mass Lynching (below) occasionally compete for the title of "largest individual mass lynching"; the distinction largely hangs (if you'll pardon the particularly grim pun) on whether the Chinese Massacre is a lynching or a race riot. Another largely Western variation on the lynch mob was the one which found or made Mexican or Native American targets: in California, according to Gonzales-Day, more than a third of lynch victims between 1850 and 1935 were of Mexican (or presumably other Hispanic) descent; about another sixth were Native Americans.

Both fractions of lynchings (as well as the Asian American proportion) were disproportionate to population, generally creating a similar (if differing in many details) pattern to the southern pattern with African Americans--the non-white race which most represented the threatening, ever-present and subjugated 'other' was the most common target. The targets merely changed with the geography.

Another nearly-full third of Western lynching victims were white: generally these were the bandits, murderers or ruffians for whom the local law enforcement saw no trouble in simply allowing mob justice to execute. A particularly strange example, and a lead-in to another category, emerges from the memoirs of Harris Newmark, published in 1916 (who calls it a "lynching-bee", which is perhaps the most comically dark term I have ever heard for the mob at a lynching). During his time in Los Angeles, four men (described as "ruffians") were heard boasting of having killed a miner outside of town. They were promptly arrested and thrown in jail; a few days later, they were hung from City Hall by around 200 or so armed vigilantes--who, as the author notes, lost all of their courage when they believed they heard Federal soldiers approach on horseback and "were seen scurrying to cover in all directions". Alas, the 'ruffians' were not saved, as it was ranchers coming to participate, and while the sheriff floated a remark of punishing the lynch mob's leaders, the reaction to the lynching was so positive that he let the matter rest.

An odd enough story on its own, certainly, and yet:

"Besides the murders lynched, there was an American boy named Wood of about eighteen years; and although he had committed no offense more vicious than the theft of some chickens, he paid the penalty with his life, it having been the verdict of the committee that while they were at it, the jail might as well be cleared of every malefactor." (p. 324-5)

This leads into the next category: the merely unfortunate, a category that also includes Henry Salzner. A mob which had previously killed William "Froggie" James in Cairo, Illinois in 1909, sought further blood; they looked for James' supposed confederate, a man named Alexander; failing to find him (as he had hidden), they settled for killing another man who happened to be in jail at the time--Salzner, who was believed to have murdered his wife with an axe. Despite the fact that the mob desired a black man's death, a white man seemed to do; the mob summarily lynched Salzner and then began arguing in the streets until the next morning, when martial law was implemented by the Illinois National Guard.

Anti-immigrant sentiment was hardly dormant during these years; exceedingly famously, eleven Italian Americans (or, in some instances, likely just Italians, as they had not been in America long enough to apply for citizenship) lynched in New Orleans in 1891. Nineteen mostly-Southern Italians had been arrested for the murder of the police chief; most of the nineteen arrested were acquitted or had mistrials, and so the mob lynched eleven (the remaining successfully hid). While Italian Americans were particularly likely to receive "extrajudicial killings", due to a poor reputation in the Gilded Age, they were not the only ones. In 1918, Duluth, MN, a town which would become famous for lynching three black men two years later, Olli Kinkkonen was lynched by a mob calling themselves the "Knights of Liberty"--in practice, something between an anti-immigrant (specifically, anti-Finnish) group and a pro-WWI enforcement organization.

This is completely leaving aside the truly individual cases, such as Joseph Smith, the founder of Mormonism, and his brother Hyum Smith (d. 1844), or 'Cattle Kate' (Ellen Liddy Watson) in Wyoming, who was lynched (with her lawyer) largely for pissing off cattle barons in Wyoming (d. 1889), or Josefa (d. 1851), a Mexican woman who murdered her rapist and became "Juanita", a violent, beautiful, dangerous woman who became the emblem of the Hispanic woman in the South, and an obvious reminder of how the protections usually afforded to women, rare as they were in the West, did not extend beyond those considered 'white'.

I hope I've slaked your desire for stories, at least.

TL;DR: Basically, a white individual could always run afoul of the 'established order' which forms the underlying 'justification' used by lynch mobs. Sometimes it was by choices; sometimes by beliefs and ideals; sometimes, by misfortune; and sometimes by births which marked them as other in the same way the African-Americans we traditionally associate with lynching had been marked at birth as 'other'.

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Cook, Lisa D. Converging to a National Lynching Database: Recent Developments and the Way Forward.

McDermott, Stacy Pratt. "An Outrageous Proceeding":

Map of White Supremacy mob violence, 1835-1964.

CSDE Lynching Database.

Account of Sen. Stephens' death, NY Times, Feb 26, 1873.

Baiamonte, John V. Jr. "Who Killa de Chief" Revisited: The Hennessey Assassination and Its Aftermath, 1890-1991

The Other Lynching in Duluth, Minnesota Public Radio, Chris Julin.

Gonzales-Day, Ken. Lynching in the West: 1850-1935..

"Sixty years in Southern California, 1853-1913, containing the reminiscences of Harris Newmark".

The Tragedy of Cattle Kate.

A history of Mexican Americans in California