Lignin, one of the three main structural biopolymers of lignocellulosic biomass, is the most abundant natural source of aromatics with a great valorization potential towards the production of fuels, chemicals, and polymers. Although kraft lignin and lignosulphonates, as byproducts of the pulp/paper industry, are available in vast amounts, other types of lignins, such as the organosolv or the hydrolysis lignin, are becoming increasingly important, as they are side-streams of new biorefinery processes aiming at the (bio)catalytic valorization of biomass sugars. Within this context, in this work, we studied the thermal (non-catalytic) and catalytic fast pyrolysis of softwood (spruce) and hardwood (birch) lignins, isolated by a hybrid organosolv–steam explosion biomass pretreatment method in order to investigate the effect of lignin origin/composition on product yields and lignin bio-oil composition. The catalysts studied were conventional microporous ZSM-5 (Zeolite Socony Mobil–5) zeolites and hierarchical ZSM-5 zeolites with intracrystal mesopores (i.e., 9 and 45 nm) or nano-sized ZSM-5 with a high external surface. All ZSM-5 zeolites were active in converting the initially produced via thermal pyrolysis alkoxy-phenols (i.e., of guaiacyl and syringyl/guaiacyl type for spruce and birch lignin, respectively) towards BTX (benzene, toluene, xylene) aromatics, alkyl-phenols and polycyclic aromatic hydrocarbons (PAHs, mainly naphthalenes), with the mesoporous ZSM-5 exhibiting higher dealkoxylation reactivity and being significantly more selective towards mono-aromatics compared to the conventional ZSM-5, for both spruce and birch lignin.