Some of the immigrant records I have been looking at are very hard to read .I seen the one for Crawford have you seen any for James Lynn travelling with Margaret ?
Rosie
That's another strange thing. The record of their arrival mentions Margaret, two step sons, Thomas and Crawford, daughter Margaret, and last, an 8 year old boy named John. I believe that is James and they made a mistake when taking down his name. Either that or the name on the 1881 Scotland census record should be John and not James. As for his age being off, Margaret's age is off as well. Perhaps it was less expensive for children to travel so they lied about their ages.
I've tried searching for a John Lynn in Scotland as well but, no luck. I think James/John died shortly after arriving in the US (and before the 1900 census) and since there were no death records required by law at that time in Pennsylvania that's why we can't locate him here.
As for the two living children you mentioned on the 1900 US census, in daughter Margaret's obit in 1939 it mentions she had a brother named William living in Ireland. He must have been one of the children born to William and Margaret before 1864.