It'd be ironic if Europe ended up banning ASML (a Dutch company) from shipping to US instead!
ASML's Dutch EUV machines depend on importing US made EUV light sources from California to build them, and depends on sales of their machines to the US to stay afloat since they're not exactly flying off the shelves domestically.
So maybe the EU is not that stupid and suicidal to cripple their economy further by cutting off one of their biggest pay-piggies for no reason.
In fact, as an anecdote to your hypothetically scenario, the US is the one with the most leverage since if they want, they can ban the export of EUV light sources to ASML and sell them instead to Canon and Nikon, sinking ASML and propping up Japan's semi industry instead, if relations sour and they see Japan as a warmer ally than the EU. Hypothetical.
FYI, the US is only 10-15% of ASML's sales. The bulk of their machines go to China, Taiwan and South Korea.
It's on US soil and subject to US laws and export controls. That's all that matters.
Mark Carney said earlier today at the EU, "the goal is not self-sufficiency, but collective resilience." It is through collective action that they can find more resilience to our American Antics.