On September 17, 2015, Walcott signed a three-year entry-level contract with the Lightning.[3]
During the 2017–18 season while playing with the Syracuse Crunch, the Lightning's AHL affiliate, he was the team's nominee for the IOA/American Specialty AHL Man of the Year.[4]
On June 7, 2018, Walcott renewed his contract with the Lightning, signing a one-year, two-way deal.[5] Prior to the 2018–19 season, Walcott was injured with the Lightning in the pre-season forcing him to miss the majority of the year. He missed 71 games with an injured shoulder before returning to play 5 games with the Crunch in the AHL.
On June 19, 2019, Walcott was re-signed to a one-year, two-way extension to remain within the Lightning organization.[6] On December 20, 2019, while playing for the Crunch, he was given a two-game suspension for abusive language towards an opponent.[7]
For the 2019–20 season, Walcott was the Crunch's nominee for the IOA/American Specialty AHL Man of the Year for the third time in his career.[8]
On April 17, 2020, Walcott was re-signed to a one-year, two-way extension with the Lightning organization.[9]
On March 9, 2021, Walcott was re-signed to a two-year, two-way extension with the Lightning organization.[10] On April 6, 2021, Walcott earned his first NHL recall with the Lightning,[11] being assigned to the Lightning's taxi squad. On May 10, 2021, Walcott made his NHL debut with the Lightning in a game against the Florida Panthers.
On December 16, 2022, Walcott set the record for most games played with the Syracuse Crunch, with 335 career games played with the Crunch, surpassing Brad Moran.