Wales made if five wins out of five in the Six Nations with a 16-9 victory over France in Cardiff.
A minute's silence was held before kick-off in memory of Davies, the 1976 Grand Slam captain, who died on Thursday at the age of 65 after a long illness and man-of-the-match Lydiate said on BBC1: "He was a legend of the game, our thoughts go this family, this one's for him."
Alex Cuthbert scored the only try of the match in the first half, while Leigh Halfpenny added the conversion and three penalties to seal the win.
Lydiate added: "We're just over the moon to be honest. The boys put their body on the line, you have to do that to win a Grand Slam.
"We're quite a young team so this is the first chance for a lot of us to win anything, we're over the moon."
Captain Sam Warburton, who went off with a shoulder injury, said: "You've got to give a lot of credit to the French, they made it very tough for us.
"But we won at the end of the day and that's what counts."