As part of the output of this classifier, I would like to know the statistical significance of the difference between two values from the lognormal. For normal data, the z-score and Standard Error can be used, but is there an equivalent method for the lognormal?

Disclaimer: I've never worked with the lognormal and may be missing some very basic instincts on the distribution (but I have research as much as possible to understand it). Let me know if you need further information about my question to understand my goals.