The Ahlfors family was Swedish-speaking, so he first attended a private school where all classes were taught in Swedish.
Ahlfors studied at University of Helsinki from 1924, graduating in 1928 having studied under Ernst Lindelöf and Rolf Nevanlinna. He completed his doctorate from the University of Helsinki in 1930.
He assisted Nevanlinna in 1929 with his work on Denjoy's conjecture on the number of asymptotic values of an entire function. In 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem. It states that the number of asymptotic values approached by an entire function of order ρ along curves in the complex plane going toward infinity is less than or equal to 2ρ.
Ahlfors worked as an associate professor at the University of Helsinki from 1933 to 1936.
In 1935 Ahlfors visited Harvard University. He returned to Finland in 1938 to take up a professorship at the University of Helsinki.
The outbreak of war led to problems although Ahlfors was unfit for military service. He was offered a post at the Swiss Federal Institute of Technology at Zurich in 1944 and finally managed to travel there in March 1945. He did not enjoy his time in Switzerland, so in 1946 he jumped at a chance to leave, returning to work at Harvard where he remained until he retired in 1977; he was William Caspar Graustein Professor of Mathematics from 1964. Ahlfors was a visiting scholar at the Institute for Advanced Study in 1962 and again in 1966.
His book Complex Analysis (1953) is the classic text on the subject and is almost certainly referenced in any more recent text which makes heavy use of complex analysis. Ahlfors wrote several other significant books, including Riemann surfaces (1960) and Conformal invariants (1973).
Lars Ahlfors was a member of the American Mathematical Society, the American Mathematical Association, Societas Scientiarum Fennica, Academia Scientiarum Fennica, the Swedish Royal Society, the National Academy of Sciences, the Academy of Sciences of the Academy of Sciences: Faculty (Harvard).
On June 22, 1933 Ahlfors married Erna Lehnert. The couple had three children - Cynthia, Vanessa and Caroline.