Isn't $\mu$ the mean? Why isn't it for the lognormal distribution? Here's the problem which confused me:
Claim sizes for an insurance coverage follow a lognormal distribution with mean 1000 and medium 800. Determine the probability that a claim will be greater than 1200.
I have given that for a lognormal distribution, E(X) = $e^{\mu + \sigma^2/2}$
Which means that E(x) is not simply $\mu$. Isn't that the definition of E(X)?
(The solution continues - since the medium is 800, $e^\mu$ = 800 ...)

$\mu$ is the mean of $\log(X)$. 
If $X$ is a Log-normally-distributed variable, then $Y=\log(X)$ is normally-distributed variable. Historically, it is common to parametrize the distribution of $Y$ it by $\mu$ and $\sigma$ of $X$. They are, however, different than the actual expectation value and standard deviation $Y$. This is because, in general,
$$\mathbb{E}(\log(X))\ne \mathbb{E}(X)$$
