I think this is subject to interpretation and it is impossible to know what “Melville believed.” But, within the context of the story itself, the lawyer does make multiple attempts to help Bartleby without resorting to force. Whether or not that is going far enough to help him is up to the reader.
The lawyer mentions early on that he believes the easiest way of life is the best, so he would be one to accept the way society runs and go with the flow. Bartleby rejects society passively. This intrigues the lawyer and eventually elicits sympathy from him. If Bartleby had actively or violently rejected the lawyer’s world, the lawyer would have had a much more clear idea of Bartleby’s motives and may have done little to help him. That being said, because Bartleby is rejecting the impersonality and indifference of the world (particularly the business world) by being impersonal himself, the lawyer can’t fight Bartleby, and if he can’t fight him, he can only ignore or help. So, maybe the question becomes; could Bartleby be helped at this point in his life. The lawyer noted that Bartleby had recently worked at the Dead Letter office and seems to conclude that Bartleby had gone beyond despair to the point of a death drive. Either the lawyer believes Bartleby is beyond help or the lawyer convinces himself that Bartleby is beyond help. If he does convince himself, then he is back to “the easiest way of life is best,” meaning the lawyer has empathy, but kind of a fake liberalism; the lawyer wants to ‘help as much as he can’ but when it gets too bizarre or difficult, he retracts back to the easy life, much in the way Bartleby retracts away from that life.