A little update:

Apparently, I was very naive when I thought a new hone will come lapped. Before I started, I lapped it only a little in order to clean it....
I decided to check if it is lapped, so I drew a grid on it with a pencil and started lapping for about a minute.
Needless to say, it wasn't lapped. Sufficed to say - it wasn't even close.
It took me 25 minutes (!) of extensive grinding until the grid wiped out from the sides of the stone (and it was not erased from the water).

Nonetheless - I didn't return to the J.H. Potter.
I took one of my Solingen (August Jorges), that has a straight edge and full hollow grind, and started the process on it:
No apparent damage to the edge, so I only did light (no pressure) stokes.
1k: 60 X strokes until arm hair shaved.
4k: 80 strokes until scratches from 1k disappeared and the strokes felt different.
8k: 40 strokes, until scratches from 4k disappeared and arm hair shaved with no pressure or effort (by simply passing the blade)
12k: 40 strokes until blade gave more resistance, and arm hair still shaving off with no effort.

Shave results:
I'm proud to say that I made a straight razor "shave ready" (by my newbie standards). :]