Before Even Clicking Onto The Link Just Knew It Was From 
Where the cat lapped up a saucer of milk (cream or whatever) and took the lace that was soaking as well.
Even by the Victorian era real handmade lace was becoming rare. Machine made stuff was rapidly out pacing both production and amount of handmade lace and often the former was of such good quality only real experts could tell the difference. Royalty and the wealthy were no exception to the wearing machine made goods. Empress Eugenie, Queen Victoria and women both high, middle and low had entire gowns,shawls, umbrellas, and so forth made from machine lace.
Many of one's vintage laundry and housekeeping manuals give a wide array of methods for cleaning "fine" lace employing everything from fuller's earth to soaps. Mind you that was all they had back then.
By the Victorian era urine for laundering and or cleaning would have gone out of fashion for all but the meanest situations. Old urine is alkaline and that is what was wanted for cleaning. Soda ash and or washing soda were available and provided the required pH without the "ick" factor as well as scent of using urine.
The problem with real lace is that it was usually made from linen thread and in it's most delicate patterns would simply not withstand the routine harsh laundering processes of the period. Even if gently hand laundered depending upon the pattern the stuff would need to be carefully dried, stretched, pulled and otherwise reshaped, and often pressed as well. Usually such things when cleaned at all were done by expert laundresses or others whom knew what they were doing. Heirloom lace like fine linens were worth quite allot then, so something missing or destroyed often couldn't be replaced. It could be resold at a good price but we're not on that now.
The other problem with lace is that it was often attached to garments,linens and so forth in that laundering methods were not compatible. This is where machine made lace out weighed use rather than the real McCoy. Bed linens, skirts, chemises, and so forth that became badly soiled or stained would require the routine harsh laundering of the time. However such processes would surely destroy lace over time (as it does today), so there was usually only one sure remedy; the lace had to be removed before the item was sent to the wash. After laundering the lace would be reattached to the item.