Petar,
I bought my LS3/6 pre-owned and they came with the stands. There's no branding on them, so I'm not sure who made them.
I suggest reaching out to Gig Harbor Audio. They will make custom stands. That's where I got the stands for my Harbeths.
Any stands made for Harbeth Super HL5 Plus should work, but there's a slight difference in size so they won't be the exact same dimensions as the base of the speakers. I think the Stirlings are a hair smaller, but don't quote me on that, it might be the other way around.