Cleanliness is a key element in growing a show coat, whether on a male or female. The Lhasa boys especially and, to be honest, sometimes the girls, tend to pee on their coats, the boys hitting the side coat and the girls the rear skirts. Whether the urine dries or is still damp, don't ever brush through coat with urine on it and expect that coat not to break.
Chances are, if you have a Lhasa you are showing, you will bathe him or her weekly before a show; however, not all of us go to shows every week, and our dogs still need to be groomed between baths. What I do with my males' side coats and the girls' rear skirts that have urine on them (or that, in the case of the girls, may be sticky with blood when they are in season), is give a partial bath before they are groomed. At home, I fill the utility sink or a dish pan with a few inches of warm water and add some rinseless shampoo (sometimes referred to as "dry" shampoo, but don't ask me why since it is a liquid!). I put the dog in the tub or dishpan and, using a sponge, wash the sticky and dirty parts of the coat (side and rear and feet generally). Since rinsing is not necessary with a "dry" shampoo, I towel the extra moisture from the hair, let the dog air dry for about a half hour, then use a dryer to complete the drying process and groom through the damp area. That accomplished, I groom the rest of the coat, brushing in layers as usual.
This cleanup takes little time and certainly saves dirty coat ends from snapping off. A quicker method if you are at a show and the dog needs a cleanup before it's groomed, is to mix some rinseless shampoo with water in a spray bottle, spray it on the hair that is sticky with urine and then towel it off. A quick blast with a blow dryer will complete the process.
(An aside here: It is not necessary to mix the rinseless shampoo with water. The directions on the shampoo will tell you to apply it directly to the coat. Most of the rinseless shampoos work great but some leave a residue that I am not happy with, even though the dog's coat is clean. I get more satisfying results when I add water to the shampoo.)