Earth atmosphere is a lot more complicated than just saying it will loose 2 degrees Celcius / 1000ft... At a certain point, the air temperature will stop to decrease with altitude. This is the tropopause, the boundary between the troposphere and the stratosphere... Going higher in the stratosphere, the temperature will even begin to increase.
I do agree with you that real atmosphere is far from being static. The tropopause height will change according to many different factors... Actually, the colder it is, the lower will be the tropopause. Generally, it will be also be lower at the earth pole than at the equator. More locally, the height of the tropopause could also vary with low/high pressure systems and even with the amount of humidity in the air below it... Consequently, you will always have a point where the temperature will stop decreasing (at the tropopause). This temperature of 56,5 deg Celcius is a mean value, but you will always have this point, at about plus or minus 10 deg Celcius (so about -55 to -65), where an increase/decrease of altitude will not result in any temperature change.
And assuming that lowering to ISA -15 like you did will result to lower temperature at tropopause is false.
First because if temperature is lower, tropopause will also be lower and youll consequently reach this point where temperature remain constant faster while climbing... Inversely, when its warmer than ISA, tropopause will be higher, so you can climb higher before reaching the tropopause. That partially explain why whatever temperature you have on the ground, the temperature will aways be somewhere -56,5C at the tropopause.
In fact, the coldest temperature that you can have at the tropopause will be over or near the equator, where the temperature is hotter and consequently, the tropopause higher...
This is confirmed by the wedsite that you posted (NOAA). Look at higher altitude, you will see that the coldest temperature at those altitude are those that are further South of the map...
So basically, -56 is a mean value, for a point somewhere between the equator and an earth pole with standard temperature (at ISA). But at the end, you will always have a point close to this -56,5C where temperature will remain constant with any altitude variation, and thats what you are seeing in DCS.
Pretty sweet that the devs have modelled this...