Do cats feel lonely when they're alone?
Won't.
Cats are solitary animals, so a single cat is rarely lonely. However, kittens are very clingy and love being with people. Especially kittens newly adopted, having just left their mother and siblings, are usually afraid in their new home and will cling to people. As cats grow older, particularly into adulthood, they often prefer to be alone. At this point, their dependence on people decreases significantly; they rarely sleep on your lap. When they were kittens, they would come running as soon as you sat down, but as they grow older, they become less interested in acknowledging you. 
If your cat becomes lethargic, sits quietly in a corner (not sleeping), sheds excessively or injures itself, or has a poor appetite or even refuses to eat, you should comfort it promptly. Give it more attention and companionship, pet it, talk to it, play with it, and give it its favorite food and canned food.