The Lumber Axe is an item that is ethier a W.I.P item or is a bug. It can be found in Dungeons added by BetterDungeons mod. Its texture looks like a rainbow. Its texture has a resemblance to another item used to craft Staffs to make the other staffs (Ice Staff, Fire Staff, etc.
If you attempt to use it, your game will crash.
If you search for it in NEI, it will not appear.
The texture is not a rainbow axe. It is just a rainbow square.