I think that as arrogant as one might say that Apple is, they have realized that the world of internet/asp services is much different than something that you totally control, in a closed environment of an OS.
They learned that the hard way through the numerous shortcomings of Me, a service which was very ambitious, but today still remains very unrealiable and has numerous shortcomings in all categories (mail, calendar, contacts, photos, idisk) when you compare it with other free alternatives.
When Me was initially announced, for a brief moment Apple had the chance to turn the market upside down, and be a leader in the ASP/cloud services arena.
Today they are not even considered a strong player - Me remains a supplementary service for only a small part of the iPhone base of users.
Consider what could have happened with Me if Apple had purchased a number of successful services (Yousendit, Dropbox, Plaxo, etc.) and combined them under one umbrella - their offering would be unmatched, they would have a brilliant team of developers, and today they would probably be leaders in the market.
I believe that this is the basic thinking behind Lala's acquisition: they are buying time, which is the next best thing after money: they are buying time they have lost, against Lala.com, Last.fm. They are buying time that they would loose if today they began to develop their own streaming service. They are buying time that it would take them to learn the mistakes others did.
With the cash reserves that Apple has right now, if it follows a clever acquisition strategy it can pretty soon gain a significant presence in internet, one that in time would rival that of Yahoo, Microsoft and perhaps even Google.
If the rumors surrounding the recent sale of AdMob are true, it seems that Apple is implementing such a plan.