Because they are historically accurate.
Prussia was very protective of the Liechtenstein region in the Middle Ages.
They were allies and they did join together in the 19th century due to the giant German Confederation.
Also, Lily was sympathetic to the Nazi movement and the Prussians in general (as they lost their “countryhood” in the 1930’s).
(And you know everyone likes a bad boy.)
In point of fact, none of this is true. Historically speaking, Liechtenstein was never closely aligned with Prussia, but rather with Austria. The Princely House descends from the Counts of Bregenz, in Southwest Germany. The territory that is now the Principality began to acquire its modern form (through the union of the Counties of Vaduz and Schellenberg) in 1434. Prussia didn’t come into existence until 1525, when the Duchy of Prussia was created out of the territory controlled by the Teutonic Order.
The Princely House’s main financial enterests were located in Moravia and Bohemia, and they aligned themselves politically with Vienna. Members of the Princely House routinely held high-ranking positions in the Austrian civil service (including Johann II’s cousin Prince Eduard circa World War I), and indeed the Princely House did not relocate to Vaduz until after the First World War.
As far as the German Confederation goes, that could hardly be more blatantly false; see, for example, the leadup to the Austro-Prussian War (which Bismarck, incidentally, attempted to blame on Liechtenstein), where Liechtenstein joined Austria in voting for a declaration of war on Prussia. Hardly the friendly relationship portrayed above.
As far as Nazi sympathies and “losing their countryhood”, Liechtenstein was never occupied during the Second World War. Hitler consistently spoke derisively about the Principality, regarding it as beneath his notice. There was in 1939 an attempted coup by Nazi sympathizers: see Beattie’s account of the VDBL’s attempted coup in 1939 for more information. It is certainly true that there were people with Nazi sympathies in the Principality, but the Liechtenstein government was consistent in its opposition to Nazi policies as far as it was able to (see also: Liechtenstein’s continued naturalization of Jewish [and other] refugees, despite German and Swiss pressure to stop; also, Franz II’s wife was part Jewish, though by the time of their marriage she was a practicing Catholic).
So, in fact, Prussia/Liechtenstein is not a historically accurate pairing.