do we know something about lost tribes? where do they live?

It is mentioned in the p'sukim and other sources that none of the ten tribes will be completely lost to the Jewish people. When the ten tribes were exiled many of them did manage to stay in Israel and joined the tribe of Yehuda and Binyamin (see Margaliyot Hayam, Sanhedrin (110b, letter 4). However, there is a disagreement in the Talmud regarding the remnants of the tribes who were exiled. The dispute is whether they will come back or not. (see Sanhedrin 110b). Some of our Gedolim, throughout the generations, tried to search for the lost tribes. Maran Harav Kook praised these efforts to search for them (see his approbation to the book Kol Hator by Rav Horvitz), as did his son Harav Tzvi Yehuda Kook (see Mashmia Yeshua, pages 202-203). There are many different theories as to where they are today, and much has been written about the topic. I'll just mention a few discussions points: The Radbaz claimed that the Jews from Ethiopia are from the tribe of Dan. Harav Ovadia Yosef (Yebia Omer, 8, Even Haezer 11) accepted his opinion and ruled that they are Jewish and don’t need to be converted. Therefore, he helped in efforts for them to come to Israel, as the Chief Sephardic Rabbi. Other poskim disagreed with Harav Ovadia about that ruling. Some have made the claim that there are groups of Jews in India that are descendants of the B'nei Menashe. However, Harav Shlomo Amar required them to go through a conversion. Some sources have made the claim that the Yemenite Jews are from Shevet Dan, (see the introduction to Milechet Shlomo by Harav Shlomo Adani). There is quite a bit more about this topic in a book called ‘Haovdim V'hanidachim’ which was translated into English. The author of this book is Harav Eliyahu Avichayil. He was a student of Harav Tzvi Yehuda Kook and made efforts during his entire life to search for the lost tribes. He passed away in 2015. All the best