[3] Lima was professor emeritus at Instituto Nacional de Matemática Pura e Aplicada[4] of which he was the director during three separate periods.

Lima has been twice recipient of the Prêmio Jabuti from the Câmara Brasileira do Livro, for his textbooks Espaços Métricos and Álgebra Linear,[5] and of the Anísio Teixeira Prize from the Ministry of Education and Sports.

Lima graduated with a bachelor's degree in mathematics from the Universidade do Brasil (today UFRJ) in 1953.

Between 1990 and 1995, he coordinated the IMPA-VITAE project, which held skills improvement courses for mathematics teachers in eleven cities from eight states throughout Brazil.

He received the grã-cruz ("Great Cross") of the Ordem Nacional do Mérito Científico ("National Order of Scientific Merit") of Brazil.