This could be Ernest Cadwell and his parents in 1920.

1920 United States Federal Census
Name: Ernest W Cadwell
Age: 43
Birth Year: abt 1877
Birthplace: Connecticut
Home in 1920: Branford, New Haven, Connecticut
Race: White
Gender: Male
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Adelia M Cadwell
Father's Birthplace: Connecticut
Mother's Birthplace: Connecticut
Home Owned: Own
Able to Read: Yes
Able to Write: Yes

Name: Adelia M Cadwell
Age: 39
Birth Year: abt 1881
Birthplace: Connecticut
Home in 1920: Branford, New Haven, Connecticut
Race: White
Gender: Female
Relation to Head of House: Wife
Marital Status: Married
Spouse's Name: Ernest W Cadwell
Father's Birthplace: New York
Mother's Birthplace: Connecticut
Able to Read: Yes
Able to Write: Yes

Name: Ernest E Cadwell
Age: 17
Birth Year: abt 1903
Birthplace: Connecticut
Home in 1920: Branford, New Haven, Connecticut
Race: White
Gender: Male
Relation to Head of House: Son
Marital Status: Single

Charles W Cadwell 15
Velvet I Cadwell 14
Russell G Cadwell 12
Kirk C Cadwell 3 [3 5/12]
----------------------------------------------------
This is the only Lamson that seems to be close. I couldn't find Ernest in 1930, but Isabelle was still single and living with her parents in 1930.

1920 United States Federal Census
Name: Isabelle Lamson
Age: 14
Birth Year: abt 1906
Birthplace: New York
Home in 1920: New Haven Ward 9, New Haven, Connecticut
Race: White
Gender: Female
Relation to Head of House: Daughter
Marital Status: Single
Father's Name: William Lamson
Father's Birthplace: New York
Mother's Name: Martha Lamson
Mother's Birthplace: New York
---------------------------------------
After I reread your post, it does say your grandfather's birth surname was Lamson, so that makes it seem like his parents were not married. Perhaps because his adoptive father was a doctor he was able to get papers that most other people would not be privy to.

FYI...Having a baby out of wedlock in 1925 was something people were ashamed of and probably took steps to hide it. Belle Lamson may have even been sent away while she was pregnant so friends and neighbors never found out.