Lenzing Tencel®is more expensive but better than any other fibre in production now. I've used it as the backdrop for all my pictures. Here's how I know my fabric is sustainable: I send my fabric to Lenzing in Austria and they verify that their fibres are in it. This certifies my clothing, and I show that by hanging the Lenzing tag on it.
The following is verifiable information on the production of fibres by the Lenzing Company(taken from Lenzing's Sustainability Report, 2017, accessed Jan 2019).
LENZING™ fibers are part of a closed natural material cycle. Through photosynthesis and without the use of herbicides, pesticides or irrigation, cellulose is produced in eucalyptus trees. Pulp derived from the harvesting of the 10-15 meter high trees produces much greater amounts of fibre than cotton per square metre of arable land. The cornerstone of Lenzing’s fabrication standards is to produce cellulose fibers from pulp without relying on the chemically complex viscose process. As such, Lenzing is a pioneer in the industry with environmentally friendly pulp bleaching. Since 1992, the Lenzing pulp production plant in Austria has produced pulp without using any chemicals containing chlorine, but with oxygen-based substances instead. NMMO, an aqueous, biodegradable, organic solvent is used in a closed loop fibre production process and recovered at a rate higher than 99 percent. The technology satisfies the Best Available Technology standards of the European Union. In this process, water is also recycled, resulting in very low emissions to the environment and much lower impact on water scarcity. Compared with other viscose fibres, Lenzing Tencel shows “substantially better” performance according to the Higg Material Sustainability Index (MSI), and it is Zero Discharge compliant (Annex 6) of OEKO-TEX® Standard 100 (a verification process which involves the reduction of hazards and risks across the entire textile production chain, from fibre production through to the make-up of products, with the goal of moving towards a greener chemistry.”https://www.oeko-tex.com/media/oeko_tex/downloads/pdf_1/DETOX_TO_ZERO_Guideline_EN.pdf)