I downloaded the Cherry Tools programming utility. I am posting the results in case anyone might be interested.
There are 3 programmable layers, they are not reached by toggle. You have to hold down a modifier (ctrl or shift) and press the key to access layers 2 and 3. (Perhaps a toggle could be jerry-rigged by programming a key with modifier-down-stroke and modifier-up-stroke, but I am not going to buy the product to find out.)
Layers 2 and 3 can only be used by storing macros on the computer. Only layer 1 can be written to the board itself.
At home, I can duplicate the LPOS's functionality with Autohotkeys. At work, the Kinesis is likely still better because of the design. However, the LPOS offers much easier programming, even restricted to 1 layer.