Hi Flyboy and thank you for your advice.
The problem actually comes from HDMI. I have a pretty wide screen ...(32''), connected to the HDMI cable and whatever I do, LB2 will always start in a ridiculous windows size (640x480).
I plugged another screen (17'' standard) with DVI ... and then finally, LB2 starts without any problem in full screen. Too bad, I would have liked to burst hellfire in HD (we can't have everything!). I will now try to set my joystick (Saitek