I will address the question quite literally, but I am not sure of the non-reversibility of the reaction in each case if the material is meant to be stable.
Hydroxyl groups of carbohydrates can be deprotonated in strongly alkaline conditions (high pK though) and even bridged by Ca(II). Likewise, phenolic hydroxyl groups of lignin can become phenoxides.
Carboxyl groups of lignin may become phenolic carboxylate salts of Ca(II). If not dissociated, calcium could bridge these macromolecules. This could be an explanation for strengthening — a mere GUESS of mine!!!
Nonetheless, this is basically talking about acid-base and solubility equilibria. If you want a (mostly) non-reversible chemical reaction, I guess a reduction of some groups of lignin could take place under proper conditions.
Also, supramolecular chemistry would be of the essence if, instead of chemical reactions, we were talking about wood-(nano)Ca(OH)2 composites.