Green’s Dictionary of Slang

lully n.1

also lally, lulley, lulleys
[? SE laundry or lilywhite]
[mid-17C–19C] (UK Und.)

1. wet or drying linen.

2. a shirt; thus dabble one’s lally v., to wash a shirt.

In compounds

lully-prigger (n.) [prig v.2 (1)] [mid-18C–late 19C]

1. one who steals from washing lines or from wherever washing has been put out to dry.

2. a thief who catches and strips a child of its clothing.

lully-prigging (n.) (also lully-snow-prigging) [prig v.2 (1)]

[mid-18C–late 19C] (UK Und.) the theft of washing.