Can lye be extracted from bamboo ash?
Yes, it's possible but as pointed out in Bamboo: an overlooked biomass resource? Biomass and Bioenergy, Vol. 19, pages 229-244:


  [bamboo] shares a number of desirable fuel characteristics with certain other bioenergy feedstocks, such as low ash content and alkali index


Potassium oxides are between 33-50% of the ash depending upon species and age of the plant.  

Potassium oxides were between 0.16-0.58% of dry matter. 

Sodium oxides were about a factor of 100 lower.