Will 16-20 1.5 volt serially connected led lights tolerate 12volt energizer battery source?
They will tolerate it so much that they won't even get started. 16 x 1.5V is 24V, anything less and the LEDs won't light. What you should do is to split your long string of 16 LEDs into several parallel strings. 8 x 1.5V is 12V, so it may look like we're there. Not. You need some headroom to control the current. That's indeed the resistor. If your LEDs need 20mA (typical for an indicator LED), then

\$ R = \dfrac{\Delta V}{I} = \dfrac{12V - 6 \times 1.5V}{20mA} = 150\Omega \$  

I used only 6 LEDs in series because for 8 the resistor value would be zero and you wouldn't have current control. A voltage drop of a couple of volts over the resistor is recommended to have a good regulation.
With 6 LEDs in a string you could make 3 strings of 6. Then you would need a total of 60mA in the given example.

The 1.5V for the LED is very low. That's usually an infrared LED. Are you sure about the voltage? What color are they?