ASML can sell if they want, but indeed the US has a lot of ways to make that unattractive. Case in point, the US has recently started pressuring the Dutch Government to prevent sales by ASML to China. I think the current stance is that they (Gov + ASML) are still considering how to proceed.
An interesting aspect though: I think the technological superiority of ASML is a big asset in these discussions. e.g. If the US would follow up on a threat of sanctions against ASML (e.g. banning US companies from working with ASML) it would hit the US semiconductor industry quite hard (particularly Intel), while non-US players (e.g. TSMC) could continue producing with euv.
In effect, they would have to go much further to keep some similarity of a level playing field: e.g banning all products containing chips produced on ASML machines. That would hit a lot more companies, many of them US based too. Creating even more reasons for the US Gov to not to take such drastic steps.
Therefore I expect that it is much more likely they'll use pressure on the EU / NL government systems to force the behaviour they want, compared to economic sanctions vs ASML.
> ASML is integrated into the dollar-based global financial system, so it will have to respect American financial sanctions
I'm no expert, but if a company wants to pay ASML in Euros, I'm pretty sure they can accept euros. The dollar is convenient, not a requirement.