Green’s Dictionary of Slang

lappy adj.

also lapps
[lap n.2 (2)]

(UK und.) drunk.

implied below .
Bailey Universal Etymological Eng. Dict.
Bailey Universal Etymological Eng. Dict. (5 edn) n.p.: lappy, in liquor, drunk. Cant.

In compounds

lappy-gag(g)er (n.)

(UK und.) one who is drunk and thus targeted for robbery.

[[UK]Proc. Old Bailey 27 Feb. 5/2: The Prisoner answer'd him, that spying a Gager that was Lapps, going along in a Rattler, he went to him, and snabbled his Poll].
[UK]Proc. Old Bailey 1 May 7/2: He saw a lappy Gager take a Ratler, so he loped after him, and snabbled his Poll: That is, He saw a Gentleman in drink take Coach; and be following the Coach, the Gentleman looking out, be snatch'd off his Wigg.
Hist. Lives and Actions of Jonathan Wild 16: A Snabbler, that Snabbles the Poll of a Lappy-gagger, is a sort of Thieves whose Business is to steal Hatts and Perrywigs.
Life and Glorious Actions of [...] Jonathan Wilde 13: The second Sort of these kind of Thieves called Snablers, are Men who make it their Business to be out late at Night, watching for Gentlemen disorder'd by Drinking (which in their canting Language is called a Lapygagger).