The Dalai Lama's view is that Buddhists should not engage in a range of sexual behavior, which includes same-sex relationships. He views homosexuality as an aberration on the same level as heterosexual couples engaging in oral sex. The Dalai Lama explained these views in his 1996 book Beyond Dogma, and in subsequent interviews clarifying what he said in the book. He has made it clear that this is purely an ethical constraint on Buddhists, and he does not believe that the state should impose any sanctions on homosexuality. He has also endorsed the principle of gay marriage for non-Buddhists.
Buddhism is such a diverse set of beliefs and practices that there really is no "classical Buddhism" with which to compare the Dalai Lama's view. The most mainstream Buddhist idea is that all sex should be avoided if possible, since it is a form of attachment, and therefore a source of suffering. However, if one must have sex, then heterosexual sex for procreation is arguably the worst form of sex, since it renews the cycle of life, which perpetuates human suffering. Having children also creates more attachment. It is notable that the first Buddha, Prince Siddhartha, abandoned his wife and child in his quest for enlightenment. Since homosexuality avoids the pitfalls of procreation, it may be regarded by many Buddhists as superior to heterosexuality.