My 4th great grandfather was Abram Lampman. Altho' a different branch than yours, mine having arrived in Canada via Quebec while yours probably travelled the south shore of Lake Ontario, crossing to Canada at Newark (Niagara Falls).
Both are descended from Peter Lampman (Landtman) He arrived in New York in 1710 and settled in Albany County, N. Y. Data can be found in the Records of the Dutch Reformed Church in that area.
I hope that this answers your question, but it would seem to me that Lydia's birth could have been in Canada.
Another Lampman has a web site "Lampman Landing", I have not looked lately, but you might find something there.