I don't think memcached was the specific reason Facebook beat LiveJournal, but I think a general hemorrhaging of competitive advantage and failure to secure additional resources was, and I think a large reason for the latter was the former. It's not really any one competitor or technology responsible for it, but the combined effect of it.
Whenever anything went wrong with LJ - server issues, PR headaches, unpopular feature decisions - a large clump of users would often very vocally say "I'm leaving", grab the opensource codebase, and start a competitor. Facebook faced all the same hiccups, but users generally stayed with them even when pissed off, because there wasn't the same option of grabbing the codebase and all your friends and opening a competing site. Moreover, it's just demoralizing to see your hard work appropriated by people who hate you and are trying to compete with you. This isn't really about Facebook, it's about DeadJournal and uJournal and Journalfen and all the other competitors.
It's also much harder to convince investors to back you when one of your primary competitive advantages is given away to anyone. I think this was probably the major problem; LJ wasn't really backable as a separate VC-funded entity, and when it was a subsidiary of Six Apart (itself VC-funded) it competed with the mothership for resources and got little attention.
The Affero GPL is partly motivated by this use case. It doesn't fully solve the problem, but it means that your competitor who grabbed your code base and set up an open-source clone, will at least have to keep open-sourcing all their stuff, too, leveling the playing field a bit. Alternately, it can serve as a kind of poison-pill to keep some competitors and would-be competitors from using your tech.
Whenever anything went wrong with LJ - server issues, PR headaches, unpopular feature decisions - a large clump of users would often very vocally say "I'm leaving", grab the opensource codebase, and start a competitor. Facebook faced all the same hiccups, but users generally stayed with them even when pissed off, because there wasn't the same option of grabbing the codebase and all your friends and opening a competing site. Moreover, it's just demoralizing to see your hard work appropriated by people who hate you and are trying to compete with you. This isn't really about Facebook, it's about DeadJournal and uJournal and Journalfen and all the other competitors.
It's also much harder to convince investors to back you when one of your primary competitive advantages is given away to anyone. I think this was probably the major problem; LJ wasn't really backable as a separate VC-funded entity, and when it was a subsidiary of Six Apart (itself VC-funded) it competed with the mothership for resources and got little attention.