Green’s Dictionary of Slang

Lady Jane n.

[euph. use of proper name]

the vagina.

[UK]Farmer & Henley Sl. and Its Analogues.
D.H. Lawrence Lady Chatterley’s Lover 219: John Thomas! Dost want her! Dost want my lady Jane?
[US]Randolph & Legman Ozark Folksongs and Folklore I 394: Pet names for the genital organs [...] ‘John Thomas’ and ‘Lady Jane’ of D.H. Lawrence’s Lady Chatterley’s Lover.