The acquisition deal emerged out of the close collaboration between the two companies, ASML said (Cymer hs been a supplier to ASML for years). It's likely that ASML determined that EUV development is so critical to the company's future that it simply must have full control over the source development.
But it's also a pretty safe bet that ASML would not have sunk $2.4 billion into Cymer if the company did not believe pretty strongly in Cymer's ability to further improve the source technology. (ASML said it would continue to buy sources from other suppliers, but it only acquired one of them).
Among the more interesting aspects of this deal, ASML will also get Cymer's deep ultraviolet (DUV) source business. ASML says it will continue to provide DUV and EUV sources to its competitors—chiefly Nikon and Cannon. But it's pretty easy to guess who will get top priority for deliveries. The Japanese lithography companies likely would prefer to buy sources from other vendors, if they can.
The painfully slow development of EUV has forced those firms with stakes at the table—Intel, Samsung, TSMC and now ASML—to get in bed with their suppliers like nothing else in recent memory. Although other lithography technologies are still in development and could step up to save the day, these four companies understand that EUV development is critical to keeping the semiconductor industry close to on pace with Moore's Law.
Considering how much ASML's future prospects are already tied to EUV, the decision to double down seems like a good move.