If you say that someone laps up something such as information or attention, you mean that they accept it eagerly, usually when you think they are being foolish for believing that it is sincere.
Their audience will lap up whatever they throw at them...
They just haven’t been to school before. They’re so eager to learn, they lap it up.
see lap 6
PHRASAL VERB : V P n (not pron) , V n P