Disclosure
Actually have several large bottles of LB "Linen Wash" part of a case purchased several years ago on fleaPay. It cost less for the lot than what stores around here charge for one bottle.
Tried contacting the maker (they are based in Florida) about what was in the stuff as have many others, and got no where. Near as one can figure out is is a private product made by special order to one of those "chemical" companies. You know the sort, you tell them what you want in the product and they handle the mixing, packaging, etc. Indeed LW's bottles are standard plastic containers anyone can purchase in from places such as ULine.
In general found LW was fine at cleaning linens that weren't soiled by anything more than bodily oils. However it is rather sudsy and may not rinse cleanly if over dosed. In my tests it did *NOT* remove blood or many of the other stains listed claimed on the packet or in advertisments. To get around this I add some liquid enzyme product (Bac-Out by Bi-O-Clean), and or make sure to pre-treat stains with an enzyme pre-treat product before things to into the wash. If stains are going to require any sort of bleaching will add one of the various oxygen based bleaches have in my stash.
Linen dealers, collectors and such have long favoured a product by P&G called "Orvus", which is simply SLS in paste form. Originally sold for bathing farm animals and horses, many like the fact it does not contain bleaches, OBAs, etc, and is a pH neutral product. So in theory Orvus, Linen Wash and the rest are supposed to good for fine and or vintage linens.
Personally feel you can launder fine or vintage linens in any detergent long as you know what you want to do, and choose the proper product to get you there.
I wouldn't wash a 100 year old handmade lace tablecloth in Tide, but I might choose Orvus, LW, or what not.
Actually two of the best products often used by those in the know for cleaning fine linens aren't made anymore. Original Ivory Liquid dish detergent, and Octagon liquid in the white bottle.