Ah, finally a question on place of birth for people from the Indian sub-continent pre-1947

My mother, now living in India, was born in Lahore in 1940....
I put "Lahore, India" when there is a pull down,
OR
"Lahore, Undivided India" when there is a write-in field.
My logic is that you can't have been born in a country that didn't exist at the time.
I guess this applies to a bunch of people, e.g. former Yugoslavia, former Soviet Republics etc.
BTW, her current passport, issued just a couple of months ago, says "Lahore, Undivided India".
Hope this helps.