I'm not entirely sure that the lignin is lost as wood dries.
The lignin is a solid matter in the wood and would not evaporate with the sap.
But it does seem to be commonly accepted that green wood is easier to steam bend.
I'm not convinced that your cling-film wrapped ash was still green though, or stayed as green as it was at first.
If it was stored for any length of time in a contained environment, with the sap in it, then surely it would have started to go even slightly mouldy?
There's no way of preventing microbes/fungal spores from landing on any object except in a completely hermetically sealed environment.
I imagine that the ash actually dried out very slowly, although not to the same degree as a kiln dried piece.
Maybe it came to some sort of equilibrium that suited the steam bending process.
I have stored green wood, mainly ash, in a shipping container that has very little ventilation.
The temperature in the container varies massively from sub-zero in winter to 40+ in summer (with the doors closed).
I've been repeatedly surprised as to how green some wood stored in there stayed despite these conditions and I put it down to lack of air flow, not temperature.
And if the wood is very fresh (especially if felled when the sap is up) then it is likely to go mouldy.
The lack of mould on your wood does suggest a lack of moisture, but I could be wrong!