dole out vs lot

dole out is not a noun while lot is a noun.

Word	Noun	Adjective	Verb	Adverb
dole out	No	No	Yes	No
lot	Yes	No	Yes	No

As verbs, dole out and lot are synonyms defined as:

Other synonyms of dole out include administer, allot, deal, deal out, dish out, dispense, distribute, mete out, parcel out, shell out.

dole out (noun)	lot (noun)
	anything (straws or pebbles etc.) taken or chosen at random
	an unofficial association of people or groups
	any collection in its entirety
	a parcel of land having fixed boundaries
	(often followed by `of') a large number or amount or extent
	your overall circumstances or condition in life (including everything that happens to you)

dole out (verb)	lot (verb)
administer or bestow, as in small portions	administer or bestow, as in small portions
	divide into lots, as of land, for example