The statement that led to the political realignment during the Great Depression is "Immigrants in urban areas voted Democrat due to Democratic political machines and the economic devastation on cities."
This is evident in that during this period, immigrants were migrating into the United States, living in the cities, and were being helped by the political machines.
The political realignment during the Great Depression occurred around the 1930s.
Option A is wrong because Franklin Roosevelt did not pass the anti-lynching law.
Option B is wrong because Democrats did not hold office for nine presidential terms but rather seven terms between 1932 to 1968 (Republicans used two terms between 1952 to 1960).
Option D is wrong because it was the Democratic party that gained from the political realignments of this period. Also, farmers supported the Democratic party, not the Republicans.
Option E is wrong because white supremacist voters from the South region supported Franklin Roosevelt and voted for him.
Hence, in this case, it is concluded that the correct answer is option C.