What would be an LDOs output if the input is its rated ouput
The parameter you are looking for is known as the Dropout Voltage - that is the minimum required difference between the input and desired output voltage in order for the regulator to maintain the correct output voltage.

This parameter is highly dependent on the load current, so you will often find a graph showing dropout voltage vs current. You simply need to add on the nominal output voltage to this value to get the corresponding minimum input voltage.

For your part, an example curve is shown on the very first page of the datasheet you linked to.

It should also be noted however the curve will also be dependent on temperature as well, so you will need to check the datasheet for further information regarding temperature effects. There are more complete graphs later in the datasheet showing dropout vs current for different temperatures for different output voltage settings. For example: