It would fall under the category of exclusive dealing.(1) Exclusive dealing is never per se illegal, but it can be as a matter of judgment before a court.
ASML would argue that it's legitimately justified because
a) there is mutual coinvestment (ASML owns 25% of Zeiss semi optics division) and thus there is symbiosis / shared risk not a simple exclusionary supply contract
b) no viable alternative customers exist for Zeiss so it doesn't matter
c) EUV litho is so tightly coupled to optics that having a single supplier is a technical necessity
d) the market was CREATED through innovation and investment across ASML and suppliers, rather than exclusionary conduct (cf. the difference between "a monopoly" and "monopolization")
The affordance of a monopoly also prevents free riding. ASML and Zeiss spent billions of dollars and decades co-developing very specific, custom-tailored technology. If a competitor could simply walk up to Zeiss and buy the lenses that ASML spent billions helping to develop, the competitor would be free riding on ASML's investment - and creating a chilling effect for future innovation.
b) no viable alternative customers exist for Zeiss so it doesn't matter
c) EUV litho is so tightly coupled to optics that having a single supplier is a technical necessity
B can also be an argument against putting exclusivity into a contract.
C is just a business decision - exclusivity due to need, not contract.
ASML would argue that it's legitimately justified because
The affordance of a monopoly also prevents free riding. ASML and Zeiss spent billions of dollars and decades co-developing very specific, custom-tailored technology. If a competitor could simply walk up to Zeiss and buy the lenses that ASML spent billions helping to develop, the competitor would be free riding on ASML's investment - and creating a chilling effect for future innovation.(1) https://en.wikipedia.org/wiki/Exclusive_dealing