The Scottish champions won all five matches during the month, keeping clean sheets in every game as the Hoops stretched their lead at the top of the table.
It is the second successive month the Northern Irishman has claimed the award, and he said: "This award shows the consistency that the players have shown this season and that last weekend's defeat [by Aberdeen in the Scottish Cup] came out of left field.
"The form in the previous two months had been impressive and all we want to do is get back to winning ways on Sunday against St Johnstone.
"The incentive now is to go unbeaten for the rest of the season. We've had Champions League football, the players have entertained all season and broken records, so we want to finish with a bit of style.
"We're 21 points clear after 24 games, so the improvement in our league form this season should not be overlooked.
"St Johnstone have given us problems in recent years and I'm sure Sunday will be tough, but I'm looking for a reaction from the players. Stevie May has had a fantastic season. I like St Johnstone. They're very consistent, and he's a bright star for them.
"We'll come out motivated on Sunday and looking to win. James Forrest may be struggling, but Charlie Mulgrew is back in training."
Celtic started the month with a 1-0 win over Partick Thistle on New Year's Day.
The Parkhead side won three of their next four matches 4-0, seeing off St Mirren, Hibernian and Kilmarnock.
Lennon's side also recorded a 3-0 triumph over Motherwell.