Do you need to determine sugar in rum? Which sugars?
I would think alcohol wouldn't have an effect on the Lane Eynon method. However, you need to be concerned regarding presence of other copper reducing compounds present in rum, e.g., phenols. An alternative would be decolorizing the sample with carbon, however, the presence of non-color phenols might still overestimate you sugar content.
Perhaps, consider an enzymatic kit? Megazyme has one for sucrose/fructose/glucose.
I agree with Bruna it wouldn't have an effect. Nevertheless, you could try with the DNS method, based on the determination of the reducing groups of each monosaccharide and the reducing ends of the chains of oligo- and polysaccharides present in the liquor samples. Reaction between 3,5- dinitrosalicylic (DNS) acid and samples is quantified by measuring absorbance at 530 nm reported by Wang et a. 2011 "High efficient conversion of cellulose to polyols with Ru/CNTs as a catalyst"