From Longman Dictionary of Contemporary Englishlap something ↔ up phrasal verb1 ENJOY/LIKE DOING somethingto enjoy something without worrying about whether it is good, true etc She’s lapping up all the attention she’s getting. The humour was lapped up by an appreciative crowd.2 if an animal laps up water, milk etc, it drinks it by putting its tongue into it The cat began to lap up the milk. → lap→ See Verb table
Examples from the Corpus
lap up• Fred, typically, was lapping it up.• It does sound silly at this distance of time, but then, green as grass, I lapped it all up.• Probably she would lap it up.• This was a most enjoyable set, with the orchestra obviously delighting in the direction and the audience lapping it up.• Francis and Christopher dissolved in laughter, lapped theirs up and declared it very good.• Induk laps it up, her tongue following the meandering trails.• Last week Katie Wood was living in the lap of luxury up in Wick.• Naturally, I can resist anything but flattery and lapped it up like a hungry cat does milk. 