MOST LEDs will illuminate some as Vf is approached. The white ones that have a 2.73 volt Vf will light up a bit at just over 2 volts. The red ones will glow over quite a range. No, it is not even close to linear and it does vary between types, but consider how a diode goes into conduction. It is certainly not an instant thing, but rather a curve. Likewise LEDs. Of course if you use a 2 digit DVM then you may not see it. I am amazed that none here seem to have ever experimented with LEDs at less than the specified nominal Vf.

 

I have illuminated LED's from a CR2032 cell that had its charge diminished to the point where it no longer would operate the device it was placed into. And as I recall, those LED's DID light up for quite a long period of time. And yes, there was no resistor on the LED. So admittedly, yes, an LED will light at lower than its Vf.

The original post wants to light LED's from a power bank that has more voltage than a single LED. Because the power bank has high current capabilities in relation to the recommended current of the LED itself, using two LED's in series - and without experimentation I can't answer this for certain - the LED's, even if their combined series Vf exceeds the power bank voltage it might still face serious current. I don't know if I want to do such an experiment, but if the TS wants to - that's up to them.

 

That is why I suggested LEDs in series. Either two in series with a small dropping resistor or three in series with no resistor.

 

I doubt that all the LEDs for this project have a forward voltage of 2.7V. Most white LEDs have a range of FV from 2.7V to 3.6V and could be anywhere in between. Right now one of my white LEDs measures 3.2V at 20mA. A red LED measures 1.9V.

 

At 20mA, I measured the Vf of hundreds of my LED's. Here's the results:

3mm LED; Clear Blue SuperBright
2.82Vf average out of 100 tested
2.80Vf min / 2.83Vf max
0.01V Standard Deviation (10mV)

5mm LED; Clear White SuperBright
2.97Vf average out of 100 tested
2.92Vf min / 3.04Vf max
0.03V Standard Deviation (30mV)

5mm LED; Clear Green SuperBright
2.92Vf average out of 100 tested
2.72Vf min / 3.03Vf max
0.11V Standard Deviation (110mV)

5mm LED; Clear Yellow SuperBright
2.01Vf average out of 100 tested
1.98Vf min / 2.07Vf max
0.03V Standard Deviation (30mV)

5mm LED; Clear Red SuperBright
1.95Vf average out of 100 tested
1.92Vf min / 1.95Vf max
0.01V Standard Deviation (10mV)

MY Blue and Red have the best (0.01) standard deviation rating, followed by White and Yellow (0.03) standard deviation rating. Green LED's had the worst standard deviation (0.11), which makes them the worst case for parallel LED's on a single resistor. Keep in mind THESE ARE MY measurements. Not yours. Your LED's will likely have a different set of numbers.