In 1933, he was awarded his laurea degree at the Scuola Normale Superiore in Pisa under the direction of Leonida Tonelli.
After a period of study from 1934 to 1935 in Germany at Monaco di Baviera under the direction of Constantin Carathéodory, he went back to Pisa at the Scuola Normale Superiore for a year, and then to Rome at the Istituto Nazionale per le Applicazioni del Calcolo, at the time directed by Mauro Picone.
In 1976 he became a citizen of the United States, while keeping close scientific contacts with the Italian mathematical community.
The department of Mathematics at the University of Michigan honoured the memory of Lamberto Cesari with the creation of a professorship chair.
He is remembered for his achievements on the Plateau's problem, on the theory of parametric minimal surfaces, on Lebesgue measure of continuous and related other variational problems: he also worked in the field of optimal control and studied periodic solutions of systems of nonlinear ordinary differential equations by using methods of nonlinear functional analysis.