Lyocell fabric made from wood. Lyocell is a fabric most know better by its brand name Tencel®. It has a soft finish, packs light and is made from cellulose (vegetable matter), or wood pulp. Tencel® branded lyocell is made from eucalyptus trees.This natural fabric is noted for its durability and strength, in addition to its eco-friendly manufacturing techniques.Lyocell is made by chipping wood, breaking down the wood fibers with the non-toxic chemical amine oxide, and then placing the material in a spinneret.his natural fabric is noted for its durability and strength, in addition to its eco-friendly manufacturing techniques. Lyocell is made by chipping wood, breaking down the wood fibers with the non-toxic chemical amine oxide, and then placing the material in a spinneret.