The Team GB midfielder completed a £15m move to Anfield from Swansea City last week after starring at the Olympic Games.
The 22-year-old has begun training with his new club, and Lucas admits that he has been impressed by Allen.
"He had a training session with us and we can see what a quality player he is so hopefully he can be a key player for us during the season," Lucas told the club's official website.
"It's one more player to fight for a place and it's really good for the club. We need more than 11 players to be successful.
"He had a good season last year and he had a great tournament in the Olympics as well. He has confidence and he has experience so hopefully he will do well for us."
Allen has eight caps for Wales.