I don't use LSP a an overall primer, though it can be used as such.
I do use it as a spot primer over putty and as a filler over small gaps and imperfections. When used as a filler it may take several applications because it shrinks as it dries.
I generally apply using a paintbrush for spot priming and a toothpick for gap filling. You can wash your paintbrush out using plain old methylated spirits.
It can also be airbrushed, but needs to be thinned if you choose to do so. Tamiya recommends their lacquer thinner, but I have found that it can be thinned using methylated spirits. Don't try using Tamiya acrylic thinner - it won't work.