lay claim vs bespeak

lay claim and bespeak both are verbs.

Word	Noun	Adjective	Verb	Adverb
lay claim	No	No	Yes	No
bespeak	No	No	Yes	No

As verbs, bespeak is a hypernym of lay claim; that is, bespeak is a word with a broader meaning than lay claim:

lay claim: demand as being one's due or property; assert one's right or title to
bespeak: express the need or desire for

Other hypernyms of lay claim include ask for, call for, quest, request.

lay claim (verb)	bespeak (verb)
demand as being one's due or property; assert one's right or title to	express the need or desire for
	be a signal for or a symptom of