The Scotland international was a 74th-minute substitute during Celtic's shock 1-0 defeat at Kilmarnock, coming on at left-back for his first Scottish Premier League appearance since October.
Brown is now in line to feature in Celtic's fifth-round clash at East End Park on Sunday.
The 24-year-old is eager for matches after undergoing a lengthy rehabilitation from his second ankle operation of 2009.
Lennon told the club's website: "Scott was excellent for an hour. He's just desperate to get back into the first team now and hopefully he'll figure at the weekend at some point.
"He's working his way back to full fitness and is a good indicator for where these other players have to be.
"He's the current Scottish player of the year, he's a full international and he led the way on the pitch.
"It's good to see senior players bringing these kids on. They will learn from playing beside guys like Scott and I have to give him credit for the attitude he showed out there. His appetite was fantastic."
Dunfermline v Celtic Win to Nil: Celtic 11/10