Tightening formaldehyde emission limits and the need for more sustainable materials have boosted research towards alternatives to urea-formaldehyde adhesives for wood-based panels. Lignin residues from biorefineries consist of a growing raw material source but lack reactivity. Two crosslinkers were tested for ammonium lignosulfonate (ALS)—bio-based furfuryl alcohol (FOH) and synthetic polymeric 4,4′-diphenylmethane diisocyanate (pMDI). The addition of mimosa tannin to ALS before crosslinking was also evaluated. The derived ALS adhesives were used for gluing 2-layered veneer samples and particleboards. Differential Scanning Calorimetry showed a reduction of curing temperature and heat for the samples with crosslinkers. Light microscopy showed that the FOH crosslinked samples had thicker bondlines and higher penetration, which occurred mainly through vessels. Tensile shear strength values of 2-layered veneer samples glued with crosslinked ALS adhesives were at the same level as the melamine reinforced urea-formaldehyde (UmF) reference. For particleboards, the FOH crosslinked samples showed a significant decrease in mechanical properties (internal bond (IB), modulus of elasticity (MOE), modulus of rupture (MOR)) and thickness swelling. For pMDI crosslinked samples, these properties increased compared to the UmF. Although the FOH crosslinked ALS samples can be classified as non-added-formaldehyde adhesives, their emissions were higher than what can be expected to be sourced from the particles.