Ancient ancestors from Ireland

Hello, I am Maya writing from Sweden.
I have some Irish or Scottish DNA, and a DNA expert says it looks like Irish.

These ancestors must have lived about 400 years ago. It is very difficult to find their names but one surname I do know.
That is Lambert.

I can only guess where in Ireland they came from. From northern part of Ireland anyway. Galway, Cavan, Laois or so on.

There is a Martin too, from 1600s.
Marcus Martin is his name. Where he came from, heaven knows. But he lived in Finland and he is my direct ancestor.

Maybe they were merchants in Galway in the 1600s? The Lamberts seem to be merchants. Maybe they fled from Ireland in troubled times?

I have asked many Irish organizations about them, so I am asking you too.
Answers are hard to find, ofcourse.

Greetings from Maya