While I did not find evidence that the name "Luman" with exactly that
spelling was ever used as a Jewish first name, my research produced
interesting results with other spellings. Although
Leman/Lehman/Lehmann is normally a surname (of German origin), a
relatively small number of Jews had been given it as a male first
name. To verify this, I found the following examples:
- Lehmann Netter. Born 1826, died 1887. Buried in Epinal, France.
- Lehmann Rueff. Born 1805, died 1881. Buried in Epinal, France.
- Lehmann Adler. Died 1892. Buried in Neu-Ulm, Germany.
- Lehmann Jehuda Lämmle. Born 12 May 1793, died 30 October 1878.
Buried in Laupheim, Germany.
- Lehmann Wurmser. Born 5 March 1860, died 11 November 1937. Buried in
Neu-Ulm, Germany. This photo  shows the tombstone of Lehmann
Wurmser and his wife at the Jewish Cemetery of Neu-Ulm:
- Leman Loeb. Died 16 January 1919, age 25. Buried at Oakland
Cemetery, Atlanta, Georgia, USA.
- Lehman S. Kahn. Born 1862, died 1911. Buried at Rose Hill Cemetery,
Evansville, Indiana, USA.
- Lehman Lowenthal. Born 1877, died 1879. Buried at Rose Hill
Cemetery, Evansville, Indiana, USA.
- Lehman Tannhauser. Born 14 February 1830, died 4 March 1890. Buried
at Temple Israel Cemetery, Paducah, Kentucky, USA.
- Lehmann Dryfuss. Born 1855, died 23 October 1878. Buried at Old
German Cemetery, Jewish Section, Kirksville, Louisiana, USA.
- Lehmann Kahn. Died 17 August 1866, age 18. Buried at Hebrew Rest
Cemetery #1, New Orleans, Louisiana, USA.
- Lehman Cohn. Born 18 April 1855, died 26 October 1914. Buried in
Natchez, Mississippi, USA.
- Leman Weil. Buried 6 September 1893, age 3 months. Buried at
Maimonides Cemetery, Brooklyn, New York, USA.
- Lehman Ullman. Died 6 December 1891, age 51. Buried at B'nai Zion
Cemetery, Titusville, Pennsylvania, USA.
- Leman Michelson. Born 16 September 1860, died 4 November 1923.
Buried in Gonzales, Texas, USA.
- Lehman Sanger. Born 26 September 1838, died 10 March 1911. Buried at
Hebrew's Rest Cemetery, Waco, Texas, USA.
- Lehman Schwartz. Born 1849, died 1884. Buried at Old Jewish
Cemetery, Hallettsville, Texas, USA.
Leman/Lehman/Lehmann is the name whose spelling comes closest to
"Luman" and which was also used as a Jewish first name. It is
interesting to note that the name itself is not of Jewish origin at
all; rather, it is a deformed variant of the German "Lehnsmann" which
means liege, vassal, feudatory. As a family name, it is very common in
Germany, but never used as a first name today. Strangely, in other
European countries, for example in France, Lehmann/Lehman/Leman is
considered a typical Jewish family name.
I can't, alas, guarantee with absolute certainty that the name "Luman"
of the person you refer to is indeed related to or derived from
Leman/Lehman/Lehmann. But it is the only reasonable connection to
Jewish names I could trace. Therefore, I hope that the information I
was able to find is interesting for you.
 Alemannia Judaica: Der jüdische Friedhof in Neu-Ulm
JewishGen Online Worldwide Burial Registry