Germany aggressively invaded Poland for their liebesraum, claiming Poland had been unfairly taken from them. At the time, the rest of the world regarded Poland as a separate nation, thus the act of war was in violation of international law. Thereafter, no act of Germany authority over Poland or its people, or for that matter any other territory it captured, could be considered legal in the context of international law. Ex post facto is kind of irrelevant when anything they did would be de facto illegal. IIUC, a great many holocaust victims were from conquered territories such as Poland.
It does not speak to any other motivation. Nazi wartime behavior in the USSR was revolting and did demand justice, and that would be true regardless of the degree of moral imperfection of their victims.
It is the same reason that the Churches have recognized the legitimacy of service performed even by priests of are in a state of mortal sin.
To some degree there is no denying that the Nuremberg Trials were an ex post facto application of the law. The Chief Justice of the SCOTUS and several associate justices and top American legal thinkers quite openly called the Nuremberg trial “victor’s justice” and criticized it vehemently. That being said, it also wasn’t simple “victor’s justice” either. Three of the four judges and the American prosecutor were both extremely keen to establish a concept of there being a type of international law to which all humans are ultimately accountable.
They wanted a genuinely fair trial, in which each defendant would be able to mount a genuine and vigorous defense against their charges. There was also a lot of legal theory justifications in which they tried to establish the idea that while, these trials were new, they really were just dealing with issues of innate human morality and law that were timeless. That centuries of treaties and expected norms of behavior internationally created a body of work from whose “penumbras” you could extrapolate that things like conspiring against peace, waging wars of aggression, crimes committed during said war, and crimes against humanity were “innately illegal.”
I don’t buy it fully, in a normal legal system you have statutes and codes that say what is illegal, and if those do not exist someone ought not be punished for violating them. But, there are arguments that in ages past individuals like pirates and marauders were generally viewed as being outside of the legal system and innately enemies of mankind, and subject to summary execution when captured.
There was a good deal of debate about how to handle the Nazi leadership. The post about Churchill is spot on, it came out in the 2000s when some British war documents became declassified. Churchill felt that the best approach would be to use an Act of Attainder to justify summarily executing top German leaders in British custody, but he was dissuaded from this. The initial plan that FDR signed onto for the denazification of Germany would have entailed the summary of execution of the highest rank “villains” of the Third Reich, but there was a lot of opposition to this for the fear of what kind of precedent it set. By the time he died FDR was inclined toward a judicial process, and Truman supported one vehemently.
It is the same reason that the Churches have recognized the legitimacy of service performed even by priests who are in a state of mortal sin.
(Fricken typos)
Then no other act committed by the USSR in eastern Poland or the Baltic States could be considered legal since those states were also aggressively invaded. Ironically, the USSR were just as guilty as Germany of the 4 charges examined at Nuremberg. Yet there they sat as judges and jury. Its also interesting to note what murderous acts werent charged. Indiscriminate bombing, for example, because then the US and the UK would also have to answer for the willful murder of civilians. There was science to the bombings.
And during the trial itself millions of human beings were being forcibly removed from their homes in massive acts of ethnic cleansing which led to hundreds of thousands of deaths.
Just to point out that the word is “Lebensraum”. “Liebesraum” would be something like “loving space” or “loving room”.
The paradox facing the vanquished Third Reich was that any standard of justice they could claim to be party to, they had violated already. 
As I understood it the Nuremberg trials were only concerned with war crimes, ie the defendants were not prosecuted for anything that happened within Germany itself before the war, as no international law would apply to such internal acts. That would be for the new German government to deal with later.