Apple's acquisition of Lala was the outcome of a brutal war with Google, a titanic struggle between behemoths straight out of a Ray Harryhausen film.
Or... not. The Wall Street Journal takes the first approach, depicting Google and Apple as moving into direct competition, and calls the first round a draw. Apple acquired La La Media, denying it to Google; meanwhile, Google assimilated mobile advertising giant AdMob, of whom Apple was also a suitor.
This, according to the Journal's analysis, shows that the two companies are moving into direct competition, having previously stuck to their own knitting and stayed out of each other's way. Google tries to make a play into Apple's iTunes turf; Apple tries to poach Google's advertising dominance—and both sides stalemate the other with preemptive corporate acquisitions.
Except that Google recently launched its own music search service. And Apple got that patent on locking down hardware to push ads to users. So one could also argue, with perhaps a bit more evidence, that Apple and Google both have their own existing strategies for which those companies would have made a good fit.
On the other hand, you don't necessarily have to look to recent acquisitions to see potential for head-to-head competition between the two. The Journal article fueled the Google phone rumor, saying that Google is pursuing handset manufacturers to build phones with "more prominent Google branding."
It's one thing for Google to ship Android to anyone who wants it; quite another for Google to sell its own phone. Considering that Google just bought the Gizmo VOIP service, and is reputedly in talks with phone manufacturers instead of, say, Verizon, that's a competition I'd be very interested to see.