Lignins released in the black liquors of kraft pulp mills are an underutilised source of aromatics. Due to their phenol oxidase activity, laccases from ligninolytic fungi are suitable biocatalysts to depolymerise kraft lignins, which are characterised by their elevated phenolic content. However, the alkaline conditions necessary to solubilise kraft lignins make it difficult to use fungal laccases whose activity is inherently acidic. We recently developed through enzyme-directed evolution high-redox potential laccases active and stable at pH 10. Here, the ability of these tailor-made alkaliphilic fungal laccases to oxidise, demethylate, and depolymerise eucalyptus kraft lignin at pH 10 is evidenced by the increment in the content of phenolic hydroxyl and carbonyl groups, the methanol released, and the appearance of lower molecular weight moieties after laccase treatment. Nonetheless, in a second assay carried out with higher enzyme and lignin concentrations, these changes were accompanied by a strong increase in the molecular weight and content of β-O-4 and β-5 linkages of the main lignin fraction, indicating that repolymerisation of the oxidised products prevails in one-pot reactions. To prevent it, we finally conducted the enzymatic reaction in a bench-scale reactor coupled to a membrane separation system and were able to prove the depolymerisation of kraft lignin by high-redox alkaliphilic laccase.