Ok, found the source of your screenshot
https://www.ledsupply.com/leds/5mm-led- ... wing-angle
And I have a screenshot you may find interesting - it's from a Kingbright green LED datasheet, but the basics should apply to most LEDs.

- L-934GD.png (17.57 KiB) Viewed 90 times
As you can see, although it's specified as having Vf of 2.2v, it starts to conduct well below that.
With the limited information you have about the orange LED (Vf = 3.6v at 10mA?), you can't do any real calculations. As you say, if it really needed 3.6v it wouldn't light, so you're now into the realm of genuine engineering - otherwise known as suck-it-and-see.
And it doesn't need the maximum current to be quite bright - your eyes are somewhat logarithmic, so doubling the amount of light doesn't make things look twice as bright. That's without taking into consideration your eyes' spectral response!
I'd try various resistor values, and select one that makes it just bright enough, but not too bright.