The 26-year-old Brazilian midfielder penned a new "long-term" deal at Anfield on Wednesday afternoon.
"It's fantastic," Ayre is quoted as saying by Sky Sports News. "He has been such a great servant to the club and I think during the period he went through with his two injuries, he put so much work into it and the club supported him through it.
"He just goes from strength to strength. We said throughout last summer and January, we wanted to keep our best, experienced players, and this is another great example of that."
Lucas joined Liverpool from Gremio in 2007 for £5m.