Not correct. Most LEDs run from 2.3Vdc up to 4Vdc, it depends on the electronic construction of the substrate. That is true for One only Light Emitting Diode. Most manufacturers will sell LED modules. These are made of several LED connected in series and or parallel and may include internal balancing resistors and some other diodes for rectification and even more complicated regulation scheme involving multiple transistors. that is why some of those modules are working of completely different voltages like 12V or 24V or even 36V and even 120VAC. See Wikipedia "LED".
As for your second question: 36VDC or 1000VDC? When connecting LED modules always follow the manufacturer specification for if you inject a 36Volts into a 24Volts module, the module may draw much more current then intended and will overheat and sooner then you wish it will permanently stop functioning.
On a more electronic point of view, if you work with a single electronic device LED and need to run it on a 12Volts DC source you would have to calculate the value of a current limiting resistor as follow: typical LED Voltage = 3Volts, Source = 12 Volts, 12-3=9 volts drop needed. Typical LED current consumption 0.02Amp, 9V/0.02A = 450 ohms. Then you would need to construct a series circuit with one LED and one 450 ohms resistor. This would consume a total of 0.02A into a sum resistance of 600 ohms. The LED would light up and will likely last for some 100000 hours if treated properly.