The 33-year-old has been without a club since the end of last season and has joined up with Brian McDermott's men - who are on the lookout for a goalscoring midfielder after selling Gylfi Sigurdsson on Tuesday.
McDermott said: "We have bought Lee in to have a look at him and he'll probably be in and around the squad for a little while.
"I watched him play out wide for Sheffield United and that didn't seem to be his position. I believe he is best in the middle of the pitch.
"I am a great believer in giving people opportunities and I know how hungry he is.
"He is a bubbly character and wants to play football so we'll see how things go."