This Frank J Lambert is listed as having been born in Skowhegan to Frank J Lambert, mother "Bessaw".Lived in IL, he possibly could be a son to your ancestor.Spouse is Josephine Marguerite Bundi from birth records of one of his sons.
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Name: Frank J. Lambert Gender: Male Burial Date: 23 Mar 1948 Burial Place: Chicago, Ill. Death Date: 19 Mar 1948 Death Place: Park Twp., St. Joseph Co., Michigan Age: 75 Birth Date: 04 Dec 1873 Birthplace: Skowhegan, Maine Occupation: Retired R. R. Man Race: White Marital Status: Widowed Father's Name: Frank Lambert Father's Birthplace: Skowhegan, Maine Mother's Name: Bessaw Mother's Birthplace: Skowhegan, Maine Indexing Project (Batch) Number: B02047-4 System Origin: Michigan-EASy Source Film Number: 1940441 Reference Number: V9ol 1 Pg 313 File 4
United States Census, 1900 Name: Frank Lambert Titles & Terms: Railroad Conductor Event: Census Event Date: 1900 Event Place: ED 96 Precinct 17 South Town Chicago city Ward 4, Cook, Illinois, Birth Date: Dec 1872 Birthplace: Maine Father's Birthplace: Maine Mother's Birthplace: Maine Race or Color: White Gender: Male Marital Status: Married Years Married: 5 Estimated Marriage Year: 1895 Mother How Many Children: 2 Number Living Children: 2 Page: 8 Sheet Letter: B Family Number: 153 Reference Number: 64 Film Number: 1240248 Digital Folder Number: 004113704 Image Number: 00131 Household Gender/Age/Birthplace Head Frank Lambert M/28/Maine/ME/ME Wife Josephine Lambert F/26/Indiana /GER/GER Son Clinton Lambert M/3/Illinois May 1897 Son Frank Lambert M/2/IllinoisMar 1898
Illinois, Cook County Bir...h Certificates, 1878-1922004271671 Image 573 Name: Lambert Birth Date: 15 Mar 1898 Birthplace: Chicago, Cook, Illinois Gender: Male Race: White Father's Name: Frank John Lambert Residence: 2829 Calumet Avenue Father's Birthplace: Maine Father's Age: 28 Occupation: Conductor Mother's Name: Josephine Margarette Brundi Mother's Birthplace: Indiana Mother's Age: 23 Birth: 2nd child Film Number: 1288015 Digital Folder Number: 4271671 Image Number: 717 Reference Number: 9486