When Lambert took charge in October the Us were in relegation trouble, but have long since banished any such fears.
He told the club's official website: "The lads have done well to get out of the relegation zone this season and next season we will push on.
"I always go back to the fact that we were down there in 21st spot when I took over.
"In the end, we have fallen just short this season and I don't like settling for second best."