There's a few discussions about Tamiya LSP in the tools forum. For all intents and purposes, it's essentially the same as Mr Surfacer 1000.
When used as a primer, it can be brushed on thinly "out of the bottle" - as it dries it will self-level very well, leaving minimal brush marks. Alternatively it can be thinned for airbrushing. It dries quite quickly when applied thinly.
If required, it can be wet sanded easily and feathers out very nicely. It can also be smoothed out without having to sand at all (meaning you can minimise damage to surrounding detail) by using a paper towel/rag moistened with denatured/ethyl alcohol. Unlike Mr Surfacer, you can clean your brushes with ethyl alcohol.
When used for seam filling, it can be brushed on or applied using an implement such as a toothpick. For this purpose, you will need to apply multiple layers as it does shrink quite considerably as it dries. It's also great for filling recessed ejector pin marks.