Lady Byron asserts that she took counsel, on this order of Lord Byron, with his family friends and physician, under the idea that it originated in insanity.

The 'Blackwood' asks, "What family friends ?' says it doesn't know of any; and asks proof.
If Lord Byron asserts that he always longed for a public investigation of the charges against him, the 'Quarterly' and 'Blackwood' quote the saying with ingenuous confidence.

They are obliged to admit that he refused to stand that public test; that he signed the deed of separation rather than meet it.

They know, also, that he could have at any time instituted suits against Lady Byron that would have brought the whole matter into court, and that he did not.

Why did he not?
The 'Quarterly' simply intimates that such suits would have been unpleasant.