Finally got to the bottom of this mystery. The Sporrong logo led us down a blind alley: just because something is made in Stockholm doesn't mean it's used there.

LV stands for
Lindholmens Varv, a former shipbuilding yard on Hisingen (northern side of the river in Gothenburg). Shipbuilding had taken place in this area since the 14th century but the yard closed finally, after years of loss, in 1985.
There are two known variants - yours with the Sporrong-stämpel, and one I have with a blank reverse.
What the token is for is still a mystery -- parking, coffee, canteen... Your guess is as good as mine.
(Source for this information is an
årsskrift from years back published by Svenska Pollettföreningen, which I was shown this morning. I won an item on Tradera yesterday and since the seller lives in Gothenburg I suggested I came and picked it up to save on postage costs and time. It turns out the seller is the owner of a coin shop here that I didn't previously know existed and has particular expertise in tokens. I spent about 2 hours talking to him this morning when I should have been doing something else! He is also planning on setting up a token research society here in the city, and I have been invited to the inaugural meeting later this month. So I may be able to shed light on various other mysterious Swedish (and indeed foreign) tokens by tapping into the other members' expertise.)