"Synthetic wood" from cellulose and lignin?
The US published application US20110190402 titled “Synthetic wood composite” appears to be very close to answering your question: “Is there research into making wood from its constituents.”  The full text can be found here: https://patentscope.wipo.int/search/en/detail.jsf?docId=US73316434&amp;tab=PCTDESCRIPTION&amp;_cid=P10-KGFN8M-16074-4
It appears to me that the short answer to your question is, Yes!
Below is part of the Summary of the Invention and Independent Claim 1.
SUMMARY OF THE INVENTION
The present invention is directed to a synthetic wood composite comprising biomimetic macromolecules and methods for the preparation thereof.
In one embodiment, the invention is a composite comprising at least two polymeric macromolecules, wherein at least one macromolecule is lignin and the other macromolecule is selected from the group consisting of cellulose and hemicellulose, or a combination thereof.
In some embodiments, the composite comprises lignin, cellulose and hemicellulose. In other embodiments, the hemicellulose is xylan.
Claim 1 – the main claim

A composite comprising lignin, cellulose and hemicellulose, wherein the cellulose content is about 40 to about 60% (w/w), the hemicellulose content is about 20 to about 40% (w/w), and the lignin content is about 10 to about 30% (w/w), wherein the lignin is selected from a kraft lignin or a lignosulfonate, wherein the hemicellulose is xylan, and wherein the composite is transparent.