Is it a must for any custom made jacket?
Polyester is indeed more durable than silk, that's why even a $8000 Kitson or Huntsman suit is sewn with cheap viscose lining from China.
Hand stitched can mean completely by hand and a hand guided machine. I don't even know what my tailor does there. Theoretically the lining needs to "settle" and be re-flattened along the bottom edges of the jacket anyway. This is because the way you wear your jacket influences the way the jacket lining gets smoothed out.
I dont think it makes a big difference but I have no aspirations to being a tailor. I have to speak with Monsieur Corvato soon, perhaps I'll ask him for you?
To my relatively untrained eye, it's always appeared to me that the lining at the (inside) bottom of my jackets (Andover and Brooks at least) were handsewn.
I asked Mr. Corvato today. He said he does both machine and hand sewing of the lining for every suit! It makes it stronger. But he says that a well done machine sewn in lining is stronger than a hand one.
If that helps at all.