lacework vs piece of work

lacework and piece of work both are nouns.

Word	Noun	Adjective	Verb	Adverb
lacework	Yes	No	No	No
piece of work	Yes	No	No	No

As nouns, piece of work is a hypernym of lacework; that is, piece of work is a word with a broader meaning than lacework:

lacework: work consisting of (or resembling) lace fabric
piece of work: a product produced or accomplished through the effort or activity or agency of a person or thing

Other hypernyms of lacework include work.

lacework (noun)	piece of work (noun)
work consisting of (or resembling) lace fabric	a product produced or accomplished through the effort or activity or agency of a person or thing