Lee has established himself as a key part of Wednesday's starting line-up under Carlos Carvalhal, with his performances in the heart of midfield setting the tone for the rest of his teammates.
And Beagrie believes that he is a player who deserves more credit that he receives, as he is not one to make the headlines.
"He's very understated," the pundit said. "He started at full-back, where his distribution was amazing, and then he found himself in the midfield area by default.
"Slowly, but surely he has become the most integral part of this team and this club. He has tremendous athleticism and he can also get a goal. He's very integral player."
Lee started for Wednesday against Hull, and he helped them pick up a point which extended their unbeaten streak to five games in all competitions.
The Owls had taken the lead through Fernando Forestieri, but they were pegged back when Abel Hernandez netted an equaliser in the second-half.
Carvalhal will be grateful that he still has Lee to pick in his side, as the 27-year-old's future was in doubt towards the back end of last campaign.
Lee's contract was set to expire at the end of the 2014/15 season, but Wednesday eventually decided to extend his deal and they are reaping the rewards for that decision now.