The UV light source that ASML uses for its lithography machine is technology that was acquired in the 2013 acquisition of San Diego-based Cymber. The tech stack for the advanced light source dates back to the "EUV LLC Initiative," led by DARPA in the mid-1990s.
US origins of the key technology here give the US a veto here regardless of ASML's Dutch headquarters.
Yes, the mechanism is effectively EAR/FDPR and you can check (https://en.wikipedia.org/wiki/Extreme_ultraviolet_lithograph...) for more detailed history, but the EUV technology ASML further developed and commercialized (no small feat) was licensed from a US Govt created consortium by which the government maintains their IP rights.
US origins of the key technology here give the US a veto here regardless of ASML's Dutch headquarters.