The word Jews use that is translated as gentile is "goy," which refers to the nations descended from Noah, as listed in Genesis.
So, "goy" means non-Jewish? Well, that would support the notion that the other tribes of the Northern Kingdom, which were not of Judah (You said the word "Jew" comes from Judah), could be refered to as gentiles.
I think we're getting confused through imprecision, which seems support Kersey's statement that Hebrew is imprecise. I think you and losttribe are engaging in the very frustrating practice of trying to to nail a drop of water to the wall.
Getting back to the point, the contention that the lost tribes of Israel, if they could be found, would be gentile from a Jewish perspective is false.
That is your opinion. Since the word "gentile" as used in the New Testament traces back to the word "whelp" in Hebrew and "nation" in Greek, and all who were in the area at the time of Jesus were Jews, you don't seem to have a reference for that opinion.
What is important is the strong evidence that Jesus would have his disciples seek out the lost tribes of Israel to bring the gospel to them. That certainly makes more sense than labored interpretaions that seem to be designed only to circumvent that notion. 