I am not going to analyze the full water footprint associated with Tencel but I do want to provide some broad facts.
Total water usage for Tencel production has been reported at around 100 m3/t (Lenzing) to 263 m3/t (Utrecht University). Even at that higher amount, Tencel production uses less water compared to conventional cotton production.
Lenzing claims Tencel production uses about a third less water compared to viscose and the Utrecht study found that the overall water usage to be about a 40% difference from viscose to Tencel - 445 m3/t and 263 m3/t respectively. Whatever the case, it seems to be less.
In regards to water footprint, Tencel has a comparatively low impact to all regenerated cellulose fibers in the Utrecht study and a significantly lower impact compared to cotton. Tencel’s biggest impact comes from pulp production with the growing of trees being a slight factor as well.
I want to leave it there as I don’t feel it’s appropriate to compare these stats to polyesters as there are so many variables. A common consensus is that lyocell has a lower impact on water footprint as fossil fuels and end of life play huge factor in polyesters total water footprint. However, the data is just not present.