object lesson vs admonition

object lesson and admonition both are nouns.

Word	Noun	Adjective	Verb	Adverb
object lesson	Yes	No	No	No
admonition	Yes	No	No	No

As nouns, admonition is a hypernym of object lesson; that is, admonition is a word with a broader meaning than object lesson:

object lesson: punishment intended as a warning to others
admonition: cautionary advice about something imminent (especially imminent danger or other unpleasantness)

Other hypernyms of object lesson include monition, warning, word of advice.

object lesson (noun)	admonition (noun)
punishment intended as a warning to others	a firm rebuke
	cautionary advice about something imminent (especially imminent danger or other unpleasantness)