1. He will have finished the work by the time you come.
2. He will have gone to Japan next week.
2-2. He will have gone to Japan by next week.
3. He will have read the book three times if he reads it again.
4. He will have lived in Chicago for ten years next year.
4-2. He will have lived in Chicago for ten years by next year.
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Would you check the sentences? Do we use 'by' or not?
Yes, sometimes use 'by.'
All except 2 are correct, and 2 would definitely be understood, with or without 'by.'