Green’s Dictionary of Slang

1. (also liver-lip) a person with thick, dark lips; often used in direct address.

1894		Wichita Dly Eagle (KS) 11 Aug. 6/5: In this city, among the colored people, there is a man called ‘Liver Lip Jack’.
1905		Chicago Eagle 20 May 1/6: Liverlips Herman [...] introduced an order for an investigation.
1918		N.Y. Tribune 7 May 9/5: McIntyre and Heath have a black face act [...] in which McIntyyre is mildly amusing as Hannah Fadocia Liverlip.
1920		H. Wiley Wildcat 156: Liver Lip [...] slammed a pair of sinful cubes.
1931		D. Runyon ‘Hold ’Em, Yale!’ in Runyon on Broadway (1954) 149: She gives old Liverlips an even bigger smile.
1939		T. Wolfe Web and the Rock 66: Outa my way, ole Liver Lips!
1968		J. Herndon Way It Spozed to Be (1970) 72: All the abusive nicknames [...] all the big lip, liver-lips, burr-heads.

2. large, dark lips.

1906		Wash. Times (DC) 5 Oct. 5/2: ‘Quit Dem Liver Lips!’ Nigger, what yo’ smakin’ dem liver lips fo’ like yo’ was eatin’ chicken?
1911		‘Cross-eyed Sallie’ in Journal of Amer. Folklore Oct. 377: She was the blackest girl in Paradise Alley. — She had liver lips an’ kidney feet.
1925		Odum & Johnson Negro and His Songs (1964) 242: Had ole gal one time, name was Cross-eyed Sally. / She was the blackest gal in Paradise Alley. / She had liver lips an’ kidney feet.
1940		Louis Jordan ‘You Run Your Mouth and I’ll Run My Business’ 🎵 Just clap your liver lips and I’ll run my business, brother.