No, they're not antonyms. A busybody is a 'nosy' person who wants to find out about other people's business which should not be their concern. [A 'nosy' person is someone who pokes his nose into other people's affairs.]
' That Mrs S is such a busybody, she's always asking me what I'm doing.'
A lazybones, as the word suggests, is a lazy, idle person, who doesn't want to make an effort. It's a familiar word, and not particularly derogatory.
'My lazybones sister hasn't got up yet, she's still in bed.'