Franco, that's the one, and that works with 1 and 1.25mm cord, and that cord is light, way lighter in combination with one of those plastic line adjusters I believe than using cord thick enough to properly hold adjustable knots.
I don't know how well it holds the 1 mm cord, but it seemed to hold it just fine in my tests, but I didn't use it for days, maybe the sheath wears, I don't know, then starts slipping, but it seemed fine.
For linenloc3's, thinnest cord I have found so far that works is the 2.2 mm glowwire from lawson equipment. That works just fine. With lineloc3's, you don't need to double over the cord to create a loop, and you can adjust the cord from 0 to full length, instead of just half length as with sliding adjuster knots or the above plastic style gizmo.
The glowire seems to be about the same thickness and roughness as the cord that tarptent uses for their lineloc3 adjusters.