Here is more about the John Lajter in Chicago. His birth place is given as "Poland," not "Ukraine."
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MARRIAGE
Name: Jan Lajter,
Male, age 23, born about 1886
Marriage Date: 25 May 1909
Marriage Place: Chicago, Cook, Illinois
Spouse Name: Pelagia Przewozna
Spouse Age: 18
FHL Film Number: 1030458
World War I Draft Registration
About 1917
Name: John Lajter
County: Cook
State: Illinois
Birth Date: 27 Sep 1885
Race: White
1930 US Census
Chicago, Cook, Illinois, USA
John Lajter 44 born about 1886 in Poland, to USA 1907
Pearl Lajter 39
Helen Lajter 18
Edward Lajter 17
Cecelia Lajter 16
Bernice Lajter 15
Chester Lajter 10
Leonard Lajter 3
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1940 US Census
Chicago, Cook, Illinois
John Lajter 55 born about 1885 in Poland
R Pearl Lajter 48
Cecelia Lajter 25
Bernice Lajter 24
Chester Lajter 20
Leonard Lajter 13
World War II Draft Registration
About 1942
Name: John Anthony Lajter
Birth Date: 27 Sep 1885
Birth Place: Poland
Residence: Chicago, Illinois
Race: White