I have to revise myself (partly).
Today I tested and measured the desklamp outlet on an old Pearl Expert, an old Tiger Touch, a new Quartz and a new Tiger Touch II.
The polarity is always as announced by Avo: Pin 1 is the negative end, Pin 2 is the positive end of the output resp. the dimmed positive voltage. (and pin 3 is linked to the chassis). That's exactly in-line with the manual, section 2.2.7:
The lamps are 12 volt DC, wired from pins 1 (negative) and 2 (positive) of the XLR
Nowadays Littlites have pin 1 connected to chassis, pins 2 and 3 go to the LED, polarity doesn't matter, see
http://www.littlite.com/contentfiledata/download/42.
The little difference is with the dimmer in the Avo console: in a Pearl Expert, it seems that the negative side of the outlet is being dimmed. That's why a standard littlite (LED between 2 and 3) cannot be dimmed but is always full-on (effectively the LED sits between chassis/ground and +12v). In order to make the LED dimmable, you need to rewire the Littlite.
The old Tiger Touch doesn't allow for dimming anyway. The LED sits between chassis (which is connected to 0v) and +12v - usually a standard littlite works.
Tiger Touch II and Quartz: again, the standard littlite LED sits (from the console's point of view) between +0...12v (dimmed) and chassis (connected to 0v). Usually it works.
Since it is not standard behaviour to use the internal ground connection as conductor, of course it is recommended to rewire your littlite: remove the bridge between pin 1 and chassis, and swop the LED wire from pin 3 to pin 1
Arena and Sapphire Touch yet need to be checked but I am sure it will be something along the same lines.