Many measured continuous quantities are in fact sums of discrete events measured with insufficient resolution (e.g. electric current) and thus conveniently modeled by continuous probability distributions, such as the normal distribution. In many cases these quantities are also essentially positive (e.g. chemical quantities that are sums of molecules), which warrants the use of log-normal distribution, often with good results. The underlying quantity is however a sum rather than a product, so using log-normal distribution seems fundamentally wrong. Is there a theoretical result justifying it?
Additional motivation for using log-normal distribution: it is a long tailed distribution, which makes it less sensitive to outliers than the normal one.