Before starting his professional career, Normantas played for KM-Citus Vilnius in the third-tier Regional Basketball League (RKL), averaging 15.9 points, 3.6 rebounds and 4.7 assists in the 2014–15 season.

[2] In September 2015, Normantas signed a long-term contract with Lietuvos rytas Vilnius of the Lithuanian Basketball League (LKL) and was subsequently loaned to BC Perlas-MRU of the National Basketball League (NKL).

[3] In his first season with the team, he averaged 10.4 points, 2.8 rebounds, 3.0 assists and 1.8 steals per game.

In the 2016–17 season, his production increased to 15.3 points, 3.7 rebounds, 4.1 assists and 2.1 steals per game.

On 15 July 2021, Normantas returned to Rytas Vilnius, signing a two-year contract.