On a somewhat similar question, did the German language spoken in West Germany grow to differ from that spoken in East Germany until reunification?
The simple answer is yes. To be more detailed, there are two classes of words that were used in the Nazi propaganda frequently: Obvious ones, like the "Lebensraum" you quoted or "Endlösung" as a chiffre for the extermination of the Jews. These disappeared pretty much immediately, because using them was a sure fire indication of being a nazi supporter, and in the climate right after the war where as a German you had to go through an "Entnazifizierungsverfahren" (basically the allied forces checked out people for different grades of involvement in the nazi state and party) nobody wanted that. Also after the GG (German constitution) came into effect in 1949, using most of these became (and still is) a punishable offense according to §130 StGB "Volksverhetzung" and §86a StGB "Verwenden von Kennzeichen verfassungswidriger Organisationen" (using anticonstitutional symbols). So these disappeared rather quickly. The other group constitutes more of a grey zone. That goes for words like "Reichskritallnacht" which were used until fairly recently as a description for the november progroms in 1938. These disappeared to my knowledge first in the historical fascism debate in the Bundesrepublik in the 80ies. As a general rule all of these words, if they are used today, are only used in quotation marks when it is clear that they refer to the Third Reich. As for the language of the Third Reich the best analysis to this day is still Victor Klemperer: Lingua Tertii Imperii - Notizbuch eines Philologen. Horst Dieter Schlosser: Sprache unterm Hakenkreuz. Eine andere Geschichte des Nationalsozialismus takes Klemperers analysis and looks exactly for what you were asking for, i.e. what happened to this language after 1945. He also looks at the official vocabulary of the DDR and what happened to it after 1989.