What are some online databases that I can search to find the pathways for sythesis of Lignin, Cellulose, GAX?
The other big metabolic database site besides Kegg is MetaCyc which certainly responds to searches for lignin and cellulose. 

The problem with lignin is that it is a very complex molecule, so in both Kegg and MetaCyc there are a many reactions involved in its synthesis. Cellulose is less complex and I have no idea what GAX is, despite an internet search. If you are so new to biochemical reactions and metabolic pathways that you cannot handle the results of a MetaCyc search on lignin you should easily be able to find articles devoted specifically to cellulose and lignin, perhaps using Wikipedia as a start.