A. Allah condemns homosexuality explicitly in the Qur'an: "Do you approach the males of humanity, leaving the wives Allah has created for you? Nay, You are a people who transgress." (26:165-166) It is the sin of the people of Lut and its Arabic word is lutiyya. Liwat is the word for sodomy, under which heading the topic of homosexuality is found in the books of fiqh.
Under shari`a both the (same-sex) sodomizer and sodomized are passible of death. The laws of other religions were similar until not so long ago. The Companions considered it so abhorrent that they subjected the culprits to burning, an extreme punishment not meted out for any other offense. As for lesbianism, the Prophet, blessings and Peace upon him said that it consisted in zina (adultery) and so it is subject to the same ruling as zina, which is death for the married, and lashes for the unmarried.
Our relaxed attitude in this day and age is purely a product of the times in which we live, where morals have been completely liquefied so that we no longer know the difference between black and white so to speak. If someone was covered with dirt from head to toes and insists that it is his way of life, we would not keep company with them for one second. What about someone who insists on his transgression when even the shari`a of Jews and Christians explicitly condemn it?