Before starting his professional career, Grigonis played in the NKL with the Žalgiris-Arvydas Sabonis school for four seasons.

On 15 May 2013, Grigonis was brought into the main Žalgiris roster for a game against BC Nizhny Novgorod in the VTB United League.

[6] On 12 June 2021, Grigonis signed a three-year contract with VTB United League champions and EuroLeague mainstays CSKA Moscow.

[11] Grigonis received an improved role in the team rotation during his second season, under the supervision of new head coach Ergin Ataman.

[14] In 2014, coach Jonas Kazlauskas included Grigonis in the preliminary 24–player candidate list for the senior national basketball team.

[15] Though, he was invited to the national team training camp for the first time only in 2016 and immediately qualified into the Olympic roster.