Sidney Laurence Pitre was born about 1910. He appears with his parents Sidney and Mary B Pitre in the 1910 census in Calciesu, Louisiana. When the census was taken in May, he was recorded as 6/12 years old, or about 6 months, so he could have been born in late 1909. 
A Lawrence S. Pitre appears in both the 1920 and 1930 census. In the 1920 census, he appears again with Sidney and Mary B. Pitre in Police Jury Ward 5, Jefferson Davis, Louisiana, and is listed as 10 years old. A sister, Esma (possibly Erma) is also listed in the household.  In the 1930, he appears listed as son with his father Sidney, again in Police Jury Ward 5, Jefferson Davis Parish. Lawrence is listed as 20 years old. Sidney is age 46 and is listed as widowed. No Esma/Erma. 
In the 1940 census, there is a Lawrence Pitre (30) listed in Fenton, Jefferson Davis Paris, Louisiana, with his wife Mary. The record indicates that he is living in the same house that he occupied in the 1930 census.
It seems likely that the Sidney L Pitre in 1910 went by Lawrence, to distinguish him from his father Sidney, unless this is an entirely coincidental Pitre family.
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MPT2-4BQ : 29 October 2015), Sydney L Pitre in household of Sydney Pitre, Police Jury Ward 2, Calcasieu, Louisiana, United States; citing enumeration district (ED) ED 32, sheet 25A, NARA microfilm publication T624 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,374,523.
"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MV7M-GV7 : 14 December 2015), Lawrence S Pitre in household of Sidney Pitre, Police Jury Ward 5, Jefferson Davis, Louisiana, United States; citing sheet 8B, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,820,616.
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:VYP9-CBV : accessed 4 October 2016), Lawrence Pitre, Fenton, Police Jury Ward 5, Jefferson Davis, Louisiana, United States; citing enumeration district (ED) 27-13, sheet 15B, family 273, Sixteenth Census of the United States, 1940, NARA digital publication T627. Records of the Bureau of the Census, 1790 - 2007, RG 29. Washington, D.C.: National Archives and Records Administration, 2012, roll 1408.
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It may be possible to confirm family relationships with Sidney Laurence by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Sidney Laurence: