Yes, sorry, Louisville, not Lexington. Ann Eliza Tryon, wid. Marshall, appears in the 1868 directory for Louisville, KY, from U.S. City Directories, 1822-1995; Louisville, Kentucky, City Directory, 1869 (Ancestry.com). I did find her death in Illinois, but not 100% certain it is her because there are others with same or similar names and dates. While Wes Tryon's book is a good place to start and is often accurate, over time documenting over 1000 Tryons I've found omissions and some errors. I have so far documented four sons of Marshall and Ann Eliza:
(1) Marshall H. Jr, b abt 1812 in New York, married Cleora Chapman 25 Oct 1835 in Hartford CT (Connecticut, Marriage Index, 1620-1926, Film Number: 001313828 from Ancestry.com), had 5 sons 1 daughter, died 8 May 1881 in Buffalo, NY Find a Grave Memorial 120955079. I suspect that supposed daughter of the elder Marshall Tryon named Cleora comes from the headstone of this branch of the family (she was a daughter-in-law), which has many Tryon names on it and on flat headstones around it.
(2) Isaac Chauncy Tryon b 31 Oct 1821 in Washington D.C. He is less certain, but I included him in this family on the basis that he is named on the Marshall H. Tryon Jr memorial headstone in Buffalo, NY, along with other members of the family, that he in earlier life shared an occupation with Marshall Tryon Jr (tailoring) and that he lived for most of his life in the Buffalo, New York area. In early life he was a tailor, the occupation he shared with Marshall H. Jr., but later he became an ordained minister of the Christian Church and was active in founding the Buffalo YWCA. He married, but never had children and aside from a mention in his obituary that his wife had died many years before him, I can't find her name anywhere.
(3) George Washington Tryon b abt 1823 in New York, drowned 16 Jul 1837 in South Glastonbury, Connecticut. Information is from a death notice which names him as "son of Mr. Marshall Tryon of New-York". This has to be Marshall Tryon Sr., as Junior would have been too young to have had a son born in 1823. His memorial (or conceivably burial) is with the rest of this family in Buffalo, NY.
(4) Frank B. Tryon b abt 1829 NY d 9 Jan 1863 in Tennessee. We have three data points for his age: census record of 1850 in Kentucky, census record of 1860, Kentucky and specification of his age upon enlistment in 1861 (33). The census records both indicate he was born in New York State. He was an agent of the American Express Company. In the 1850 census Frank appears with an Eliza Tryon, aged 30 (a sister?). His occupation is given as "none". I have not, so far, found any further documentation of this possible sister Eliza, who would have been born about 1820, and no relationship is noted in the 1850 census. The name is so common it's difficult to track her down among the many Eliza Tryons who appear in later censuses, and possibly she married.
As to Ann Eliza's maiden name, the variants are Hawk, Hawke and Hawkes, but all come from family trees not supported by documentary evidence. Looking for an Ann Eliza Hawk/Hawke/Hawkes in early New York yields only a daughter Ann of a Peter Hawk, but the single reference to Peter Hawk with a daughter named Ann is very inconclusive.