But how now - that box is unable to count until three...!

How should a table look to achieve that?
Three switches are to be used and still two lamps...
left switch middle switch right switch green lamp red lamp A + B + C = D E and we
think
up up up off off O + O + O = O O "zero"
up up down off ON O + O + I = O I "one"
up down up off ON O + I + O = O I "one"
down up up off ON I + O + O = O I "one"
up down down ON off O + I + 1 = I O "two"
down up down ON off I + O + I = I O "two"
down down up ON off I + I + O = I O "two"
down down down ON ON I + I + I = I I "three"

And how could a box look to achieve that?

move on