Wikipedia states, that the city of Salzburg (Austria) was called „Stadt der Lebensforschung“ as honorary city title.
Is there any source that describes why?
I strongly doubt labeling Salzburg as "Stadt der Lebensforschung" was some sort of official honorary title. As far as I see, the only source for this title is an article in the "Salzburger Landeszeitung" (in those times, an Austrian national socialist's newspaper; not to be confused with a modern-day government gazette holding the same name) by Eduard Paul Tratz - Austrian zoologist and founder of Salzburg's "Haus der Natur". The article is titled "Salzburg - Stadt der Lebensforschung". Tratz joined the SS and the infamous "Ahnenerbe" society in 1938/39; maybe he planned to enlarge the "Haus der Natur" towards an institute for "Darstellende und angewandte Naturkunde", as one of the prospective "Ahnenerbe" institutes.
There's no evidence that "Stadt der Lebensforschung" was in fact an "official" honorary title of Salzburg (see also the german Wikipedia on such honorary titles). Theoretically, it would have been possible to attribute such a title to Salzburg. In 1935, in Germany the "Deutsche Gemeindeordnung" was issued, implementing the "Führerprinzip" also on a local level. § 9 of the Gemeindeordnung stated regarding the names of municipalities:
"(...) Der Reichsstatthalter kann nach Anhörung der Gemeinde Bezeichnungen verleihen oder ändern".
Here we have the legal base to assign official honorary titles to a town. The Gemeindeordnung was applicable in Austria, too, since October 1938.
But, in contrast to other towns who received such a "honorary title", there is no evidence regarding Salzburg. IMHO, the strongest proof for this is how the Reichsgesetzblatt (abbr. RGBl) referred to diverse towns. There were different statutes issued concering matters of, e.g, Munich, Nuremberg or Salzburg. In the case of Munich or Nuremberg, in the statute's title the "honorary title" of the town was used, but not in the case of Salzburg. For example, there are two statues dating from january 16, 1942, the first referring to Salzburg, the second to Munich:
Zweiter Erlass des Führers und Reichskanzlers über städtebauliche Maßnahmen in der Stadt Salzburg. (RGBl I 1942, 26)
Zweiter Erlass des Führers über die Neugestaltung der Hauptstadt der Bewegung. (RGBl I 1942, 45)
And a little later (march 3, 1942), regarding Nuremberg:
Zweiter Erlass des Führers und Reichskanzlers über städtebauliche Maßnahmen in der Stadt der Reichsparteitage Nürnberg. (RGBl I 1942, 115)
This is backed by the evidence of Google Book's NGram search. For the official "honorary titles", there's a obvious peak around 1940; in contrary, for the title "Stadt der Lebensforschung", the NGram index isn't able to provide even a single hit.
So, it seems that this "title" wasn't actually used by anyone, neither official sources nor other contemporary publications.
In fact, there wasn't actually any reason to label Salzburg as "Stadt der Lebensforschung". It's quite doubtful if "Lebensforschung" could be equalized with "life sciences" / "natural sciences" - I don't think that this identification is justified. Nevertheless, before 1938, there wasn't any notable research institution situated in Salzburg devoted to natural sciences / life sciences. Salzburg was certainly not seen as a "center of life sciences", neither by its inhabitants nor from outside. The "Große Brockhaus", dating from 1935, labeled Salzburg as "Markt- and ruhige Wohnstadt, Verwaltungssitz und bedeutenden Fremdenverkehrsplatz". Regarding educational institutes, the Brockhaus states:
"Die 1623 gegründete Universität wurde 1810 aufgelöst. doch besteht noch eine theol. Fakultät und ein Priesterseminar. S. hat ferner: 2 Gymnasien, 2 Realgymnasien, Realschule, Lehrer- und Lehrerinnenbildungsanstalt, Handels- und Gewerbeschule, Hebammenanstalt, 5 geistl. Erziehungsanstalten, städt. Museum, Mozartmuseum, naturwissenschaftliche Sammlung, Musikschule Mozarteum, Künsterhaus, Theater, Studienbibliothek (128021 Bde.)".
The "Volks-Brockhaus" (1943) points to the "Reichsmusikhochschule Mozarteum" and the Festspielhaus (Salzburger Festspiele); but for both encyclopediae, there was no reason to label it as "center of natural sciences". This would rather apply to other German towns (for example, Heidelberg or Tübingen) who would have raised heavy objections against such a "official" title attributed to a town almost totally lacking any scientific merits. From the point of view of the German government, such a title would rather fit to one of the new "Reichsuniversitäten", esp. Straßburg with its medical faculty. There's only the "Naturwissenschaftliche Sammlung", presumably referring to the "Haus der Natur" (see below) - but that museum wan't primarily a scientific institution.
As interim result, we may state that Salzburg wasn't a widely (nationwide) acknowledged centre of life sciences, and there's no evidence that the title was actually used.
As far as i see, there's only one single publication that actually used the label "Stadt der Lebensforschung", as mentioned above. In that long and detailed article, Tratz refers to a meeting named "Wissenschaftswoche" that took place in 1939 at Salzburg, organized by the infamous "Ahnenerbe" society (the 1940 meeting had to be canceled because of the German assault on France):
Die Forschungs- und Lehrgemeinschaft „Das Ahnenerbe" des Reichsführers SS Himmler trat in Salzburg vor einem Jahre mit ihrer ersten „Wissenschaftswoche" erstmalig als akademische Künderin eines Teiles ihrer Forschungsleistungen vor die europäische Öffentlichkeit. (...) Von selbst bilden sich (...) hier und dort dauernde Sammelpunkte der Arbeit, und hierzu gehört bekanntlich auch das Salzburger „Haus der Natur"; dies ist sogar dazu ausersehen, das Mutterhaus einer ganzen Reihe von Instituten zu werden, die sich fachlich wie örtlich um die biologische Zentrale gruppieren werden. (Salzburger Landeszeitung, 31. August 1940, S. 12 - reprinted in Floirmair et al., "Nationalsozialismus und Krieg", 1993, p. 196)
This refers to the "Haus der Natur", founded by Tratz and others in the year 1924 as "Salzburger Museum für darstellende und angewandte Naturkunde" (museum for exhibitve and applied natural history), renamed to "Haus der Natur" in the year 1936. According to Tratz, his museum was designated as nucleus for a number of scientific institutions, all connected to the "Ahnenerbe" society, thus making Salzburg in fact a centre of "Lebensforschung" - not to be confused with "common" life sciences or natural history, but rather some sort of "science" propagated by the Nazis as basis for their racist ideology (this, IMHO, makes clear why there are only few references to the "Stadt der Lebensforschung" after 1945...).
This "Lebensforschung" was part of an ideological policy, supported and boosted by Friedrich Rainer, in those days Gauleiter of the Salzburg area. Rainer tried hard to win Othenio Abel as head of a proposed research institute named "Institut für Lebensgeschichte". In 1940, Abel was Emeritus professor, and he was connected to the "Haus der Natur". As long-term goal, Rainer dreamed of a SS university to be founded in Salzburg that should be closely linked to the "Ahnenerbe" society. All these plans were never implemented - so, after 1945, only the "Haus der Natur" remained, with Tratz as head again after 1949.
As far as I see, Salzburg wasn't officially labeled "Stadt der Lebensforschung" by the Nazi goverment. This label was rather used by people connected to the "Ahnenerbe" society and the SS, denoting a project to develop Salzburg as home of some "research" institutes - but that project was never implemented at all.
It is because Salzburg was the center of life sciences, or what was formerly called "natural science," in Germany. This includes the study of medicine. Paracelsus settled in Salzburg and this is the city he is associated with. The Association of German Naturalists and Physicians frequently met at Salzburg. There was a famous Lyzeum in Salzburg dedicated to medicine and natural science. Salzburg has always had a well-regarded medical school. This is not to say other places had good natural science, but basically the two things Salzburg was famous for was being the hometown of Mozart and being a center for the study of medicine and the natural sciences.
In Germany under the Nazi regime it was somewhat of a fad to give both places and people nicknames or unofficial titles as a sort of a role label. The idea was that everything and everybody was to be employed in some specific way and role, noone left out. The Germans actually used to joke about this at the time and give each other silly titles, like Herr Meister Car Polisher, or whatever.