[1][2] Lyra was an important mathematician in his area, his course Introdução à Topologia Algébrica was taught in the first Colóquio Brasileiro de Matemática[3] and would become the first text in this field written in Brazilian Portuguese.
[1] After the death of his father, his mother married a Wall Street stockbroker and, together, the couple moved to New York City with Lyra and his younger brother.
Around the age of 15, Lyra met the researcher and founder of the Institute of New York University, Richard Courant (1888–1972), during one of his daily train journeys.
[1][2] By the end of middle school, Lyra had the opportunity to obtain US citizenship and follow the wishes of his stepfather who wanted to see him work in Wall Street and study in a university which would accept him, including Yale.
In 1945, returning to Brazil after the end of the Second World War, Lyra enlisted himself in the Brazilian Army to continue his path to citizenship and spend some time living with his brothers from his father's earlier marriage as guardians until he turned 18.
The following year, he would move to São Paulo, living in the home of Manuel Tavares, a lawyer and friend of the family, and soon begin his study of Mathematics.
During this time, he would meet French mathematicians André Weil (1906–1998) and Jean Dieudonné (1906–1992), and have lectures with Professor Cândido Lima da Silva Dias (1913–1998) on the topic of algebraic topology, the area of study he would pursue during the rest of his career.
With this, he travelled to France in 1952 to take part in a postgraduate program with funding from the Conselho Nacional de Pesquisas (CNPq).
He met and studied with Henri Cartan and participated in seminars and watched Hurewicz's lectures on homotopy in the Collège de France in Paris.
After meeting Lyra, they began their relationship and they moved to the Hotel des Grands Hommes, in Paris, where they would remain until the end of their stay in France.
Influenced by a visiting professor at the USP, Alexander Grothendieck, Carlos learnt about cohomology, furthering his interest of topology.
He received funding from the Rockefeller Foundation in 1961 and moved his family to New Jersey, where he visited the Institute for Advanced Study at Princeton.
It was in the first Colóquio Brasileiro de Matemática in which he led a course based on his doctorate (Introdução à Topologia Algébrica), and on the fifth and seventh he presented once again.
This commission was composed of the professors: Emilio Lluis (Mexico), Orlando Villamayor (Argentina) and Carlos Benjamin de Lyra (Brazil).
[1][3] Lyra was described as a socialist intellectual and, between the years of 1950 and 1955, was a member of the Partido Socialista Brasileiro, having such colleagues as Paul Singer, Febus Gikovate, among others.