I'm not sure if you are looking for living relatives or his ancestry from your question. His death record lists father as George Lamb, spouse Alice. On other records, mother is Elizabeth, he has a wife Cora Frances McKim, son George Mack. In census data he has a brother John. Click the bottom link to see more records. You can plug in the names/dates/locations into the free search tool at: https://familysearch.org/search to find more on these individuals.
Illinois, Cook County Deaths
Citing this Record: "Illinois, Cook County Deaths, 1878-1939, 1959-1995", index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/QV9J-M4YZ), Jay K Lamb, 1962.
Name: Jay K Lamb
Death: 04 Jan 1962 Chicago, Cook, IL
Address: 81st Avenue and 124th Street
White Male Age: 84 Married
Birth: 28 Nov 1877 DePere, , Wisconsin
Funeral Home: Lackore Nichols And Lane
Cemetery: Mt Hope
Father: George W Lamb
Spouse: Alice Lamb
Entry Number: 430
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