David Lurie and Lucy are each figures of isolation in Disgrace.
At the opening of the novel, David Lurie describes his attitude toward teaching, saying that he feels out of place at the university. Though he talks about his interactions with students, he does not identify or connect with them. He is, essentially, isolated in his profession (or by his profession).
When Lurie carries on his affair with Soroya, he finds that he can no longer continue sleeping with her after he sees her children. His relationship with her is only possible in the context of literal and actual isolation. Once she is seen in the context of a "real" life, Lurie stops seeing her.
Arguably the most poignant example of isolation comes when Lurie leaves the city. As a self-professed city person, Lurie's journey into the countryside is an exile, a significant and forced departure from the life he has known.
Lucy chooses to live in the country among people of another culture and she is also homosexual. Both of these facts situate her in modes of isolation.