I just found out that my ancestors were Jewish. Is it possible that The LORD is leaving a remnant without them knowing it? Could a lot of people who think they're Gentile actually be Jewish and be part of the remnant?
The remnant of Israel is the "believing" and faithful element among all Jews. In the days prior to Christ, the remnant were best described by the Lord Himself in 1Kings 19, when He said to Elijah in 1Kings 19:18:
In Elijah's day, those who had not "bowed to Baal" were the faithful remnant of Israel. They were the remnant because they held to God's Law and did not engage in the idol worship which dominated Israel in that day.
Now that the Messiah has been revealed in Person of Jesus Christ, the faithful remnant of Israel will be those Jews who have come to know Jesus as Messiah and become part of the Church. Though these Jews are now joined with Gentiles in the Body of Christ, they are also Jews and therefore are the remnant. Paul speaks of the Jews who have come to faith in Christ as the remnant of Israel in Romans 11:5:
In the same way then, there has also come to be at the present time a remnant according to God’s gracious choice.
Who then can be considered a part of this Jewish remnant? A Jew is anyone who is descended from Abraham, so the Israelites maintained scrupulously accurate genealogies to establish who was a Jew. These records were held in the Temple, but following the destruction of Israel's records in AD70, the Jews have determined who is Jew by the identity of the mother. Simply put, you are considered Jewish if your mother was Jewish. If a Jewish man marries a Gentile woman, then her children are no longer considered Jewish.
In your case, you would be considered Jewish (and hence a part of the remnant) if you had a Jewish mother and were a practicing (religiously orthodox) Jew prior to your conversion to Christianity. Otherwise, you are a Gentile despite having Jewish ancestors.
To the larger question of how the lost tribes of Israel are accounted in this day and in the future, we do not believe these tribes will be "found" among the Gentiles. The lost tribes continue to exist today among the practicing Jews of the world. Otherwise, they are no longer Jewish. Remember, a Jew must continue to marry within the Jewish nation to be considered Jewish and to remain eligible for the promises (Deut 7:1-12).
Instead we believe these lost tribes are still scattered among the practicing Jews in the world, though they themselves may be unaware of their tribal affiliations. Once the Spirit begins to work with the Jewish people again during Tribulation, then the tribes will re-emerge again to create the 144,000 evangelists.