Why does such a lamp and two battery circuit not work?
Why does such circuit not work?


It's not a circuit to begin with since there is no closed path around which charge can flow through the lamp.

Let's try a different route to see this result.  To make your 'circuit' an actual circuit, place a resistor between the "remaining - and + poles" as so







simulate this circuit &ndash; Schematic created using CircuitLab

Using elementary circuit laws, we can find the potential difference across the lamp to be

$$V_{\mathrm{lamp1}} = (6\:\mathrm{V} + 6\:\mathrm{V})\cdot \frac{100}{R_1 + 100}$$

So, for example, if \$R_1 = 0\:\Omega\$ then

$$V_{\mathrm{lamp1}} = 12\:\mathrm{V} \cdot \frac{100}{0 + 100} = 12\:\mathrm{V}$$

But, as the resistance of \$R_1\$ is increased, the potential difference across the lamp must decrease.

For example, if \$R_1 = 1\: \mathrm{M\Omega}\$, then

$$V_{\mathrm{lamp1}} = 12\:\mathrm{V} \frac{100}{1,000,000 + 100} =  0.012 \: \mathrm{V}$$

Setting \$R_1 = \infty\$ is equivalent to specifying that the "- and + poles are not connected".

In that case the potential difference across the lamp is

$$V_{\mathrm{lamp1}} = 12\:\mathrm{V} \frac{100}{\infty + 100} =  0 \: \mathrm{V}$$

in contradiction to the claim "So there is a potential difference between across the lamp".  In fact, there is no potential difference across the lamp and, as stated earlier, it is for the simple reason that there is no closed path around which charge can flow through the lamp.