The $\mu$ and $\sigma^2$ parameters are the population mean and variance of the *logs* of the [lognormal](http://en.wikipedia.org/wiki/Log-normal_distribution) random variable with those parameters. 

Your equations for them are correct - they're how the population mean and variance of the lognormal relate to the mean and variance of the log-variable.

Equating those expressions to the sample mean and variance would be a reasonable thing to do --- indeed, it's essentially [method-of-moments](http://en.wikipedia.org/wiki/Method_of_moments_%28statistics%29).

Those equations are rather straightforward to solve.

Divide the variance by the square of the mean, you get an equation in only $\sigma^2$ (one that's easily solved).

Then once you have solved that to get an estimate of $\sigma^2$, it's simple to substitute it back into the first equation to solve for your estimate of $\mu$.

If you want explicit formulas, see [here](http://en.wikipedia.org/wiki/Log-normal_distribution#Notation)