Here is the 01 September 1912 arrival of a man named Peter Lajter at Port Huron, Michigan, USA, mentioned earlier. Sadly, there is no information to help us know if he is "your" Peter.
I do not know if this is a family member for you. I will put this here for now. Later, I can delete it (if it is not your family).
Name of Deceased: Lajter (Layter), Antonina
Gender: F (Female)
Death Date: 7 Mar 2005
Obituary Date: 9 Nov 2010
Newspaper Location: Canada
Birth Place: Ukraine
Spouse's Name: John Lajter
Parents' Names: Canada
Childrens' Names: Nina Layter-Hermelin and her husband Jean Pierre Hermelin (Ajax), and Anna Layter (Ajax)
Siblings' Names: Mary Shulga (Whitby), Olga Goreglad (Oshawa) and the late Leon Makowchik