Some good resources in R: http://www.stat.ucdavis.edu/~hiwang/teaching/10fall/R_tutori... http://www.stat.ucdavis.edu/~hiwang/teaching/10fall/R_tutori...
In particular, what it allows you to do is to estimate the future duration -- saying that your average LTV is the 6 months of average revenue from your existing customers as the article suggests is incomplete, because the portion of customers who haven't lapsed will continue to provide revenue. With survival analysis, you can estimate the full durational curve to get this right.
Future value generally doesn't matter a huge amount if you're just looking for gross differences across segments, but anything you're getting particularly precise on (like when you want to figure out allowable cost for advertising based acquisitions), needs to take this into account.
There are tons of other great lessons to apply to "regular" business from actuarial science.