How do I know if there is internal resistance in an LED?
LED's do have some internal resistance. Without consulting or knowing the data sheets for your particular components, I suspect what's happening is because you've got 2 in series, there's very little current because most of the voltage is being dropped. Typically in an led circuit, the equation to calculate current is 

i=(Vsupply-Vled)/R 

Where Vsupply is your input voltage and Vled is your LED's forward voltage drop. This can vary and really depends on the LED used and you'd need to consult the datasheets of the LED. You can read more about it here. With 2 Leds in series, it probably approaches the full 1.5v drop. Most LED's have voltage drops larger than 1.5V for full conduction. So there's very little current because the LED isn't fully conducting yet and this is why it's the case with either 1 or 2 LED's in series. A resistor would only need to be added when the LED has reached full conduction, which will be when Vsupply>Vled