Estimating mean and standard deviation of lognormal distribution between two points

This is a statistical question. Let's say I have two numbers. One is a lower bound and the other is a point estimate to the right of the lower bound. Now, let's say I want to be able to estimate the mean and standard deviation of a lognormal distribution, where 95% of the density falls within the range of the lower bound and the point estimate. Concomitantly, can an exponential distribution be described in the same fashion?

Any help would be greatly appreciated.

JB