Converting the log (Stellar Luminosity/Solar Luminosity) and the log of the plus and minus variation
You're completely right, except that the authors, as far as I can see, don't specify whether the central value (i.e. $\log L = 2.01$, or $L = 102$) is the most likely value (i.e. the mode), or the average, or the median. My guess is it's the average, but especially for logarithmically distributed values, my opinion is that the median would makes more sense to quote, since in that case you'll get the same result whether you take the median of $L$ or of $\log L$.