We can only assume that Boo is a lonely man since he keeps quiet on the subject. The children certainly assume that he is lonely, staying shut up in the Radley house during the day and only coming out at night when no one else can see him. Scout thinks Boo must be lonely:
... Mayella Ewell must have been the loneliest person in the world. She was even lonelier than Boo Radley... (Chapter 19)
Like Mayella, Boo has no real friends aside from his brother Nathan. Boo must recognize the children's curiosity about him, and he reciprocates by leaving gifts in their secret knothole--an act of friendship no doubt motivated by his own loneliness. Boo's reclusiveness is originally forced upon him by his father, who shuts him up inside the house as punishment following his arrest as a teenager. But Boo's reclusiveness becomes self-imposed after his parents' deaths, and Dill believes he knows why.
"Maybe he doesn't have anywhere to run off to..." (Chapter 14)
Boo must know about the stories that are spread about him by the townspeople, and he maintains his outcast status because, according to Jem,
"... he wants to stay inside." (Chapter 23)
Boo's loneliness is not strong enough to seek friendship in the outside world, even after his heroic actions save the children from Bob Ewell. After Scout walks him home, Boo disappears inside,
... and shut the door behind him. I never saw him again. (Chapter 31)
Boo Radley is a lonely man because he is isolated in his house and has no visitors. The neighborhood views him as a social outcast.
When Boo was a teenager, he went around with the Cunninghams from Old Sarum. One night, this group became too rowdy, so they were apprehended by Maycomb's "ancient beadle," a minor official named Conner. Mr. Conner charged them with disturbing the peace, using abusive and profane language, and disorderly conduct, along with assault. After the boys' sentencing in court, Boo's sanctimonious father would not permit Boo to attend the state's industrial school, so he sequestered Arthur "Boo" Radley in his own home.
That Boo may well be lonely in his solitary confinement because he is friendless is apparent when the children hear him laughing inside the Radley house, indicating that the solitary man has been watching them. They have been playing with an old tire in which they have stowed little Scout inside. The boys push her so hard that she rolls into the Radley yard near the steps.
Through all the head-shaking, quelling of nausea and Jem-yelling, I had heard another sound, so low I could not have heard it from the side walk. Someone inside the house was laughing (Chapter 4).
Later, the curious Scout asks Miss Maudie about the Radley house, and the wise woman replies in a manner that suggests Boo's isolation and loneliness,
"No, child," she said, "that is a sad house. I remember Arthur Radley when he was a boy. He always spoke nicely to me, no matter what folks said he did" (Chapter 5).
As the summer progresses, Boo Radley attempts social interaction with the children when he sows Jem's pants after Jem sneaks onto the Radleys' porch one evening.
Seeing the shadow of Nathan Radley on the porch, Jem tries to run away, but he catches his pants on the barbed wire and tears them. Since these pants are also caught on the fence, Jem slips out of them and runs home. Later that night when he sneaks back to find his pants, he finds they are stitched up for him. Jem tells Scout, "It's almost like--" and she finishes, "somebody knew you were comin' back for 'em" (Chapter 7).
Boo certainly has hoped Jem would return, since after this incident, Boo begins to put little items in the knothole of a tree that the children pass on their way home from school. Clearly, this isolated man is lonely, as he reaches out to the Finch children, of whom he has carved small soap figures.
Boo's having derived pleasure from his vicarious experiences of observing the children demonstrates that he is alone in his house and watching outside where there is human interaction. His isolation is real as he continues to watch Jem and Scout engage with one another and traverse the neighborhood.
Finally, Boo emerges from his house because he senses the urgency of coming to the aid of Jem and Scout when Bob Ewell attacks them. The reclusive and friendless Arthur "Boo" Radley saves Jem and Scout's lives. Scout takes his arm as Boo returns to his house, goes inside, and shuts the door.