Spitzer was born to a Presbyterian family in Toledo, Ohio, the son of Lyman Spitzer Sr. and Blanche Carey (née Brumback). Through his paternal grandmother, he was related to inventor Eli Whitney.Ancestry of Gov. Bill Richardson Spitzer graduated from Scott High School. He then attended Phillips Academy from 1929 to 1931 and went on to Yale College, where he graduated Phi Beta Kappa in 1935 and was a member of Skull and Bones. During a year of study at Cambridge University, he was influenced by Arthur Eddington and the young Subrahmanyan Chandrasekhar. Returning to the U.S., Spitzer received his Ph.D. in physics from Princeton University in 1938 after completing a doctoral dissertation, titled "The spectra of late supergiant stars", under the direction of Henry Norris Russell.
