I can't remember since I only saw one playthrough, but was that the arm that was bit? Because I thought he felt it getting weaker and all. If it is, then maybe it was to make sure he had enough of a strong grip on the weapon.
"Kaiouken x100 + Bankai Moe Moe Kyun Just As Planned No Jutsu!"... I won again. ~The Official Shiny Glaceon In The Pokemon BW2 Board~
Lee talks to Christa and Omid earlier in the episode about how he is starting to loose feeling in his arm and he knows that he's running out of time, so when he picks up that shard of glass, I think it's Lee basically saying to himself:
"You ain't dead yet and you ain't gonna die til that Little girl is safe."
I am the true essence of Evil's bane. I am the Fierce Deity and I have risen again to kick your ass