The Cambridge dictionary definition is the correct one. The presence of "it" is a variant or an irrelevance (remember that the Stevenson work is 100 years old now - languages change).
From the context it is obvious that Jim has told the authorities in the matter of his bankruptcy that the narrator was not a partner, but merely a naive employee, and therefore his assets are not part of the bankruptcy - leaving the narrator with plenty of money instead of owing plenty of money. It also seems that was not actually the case ( based on what the narrator says) so "make it out" means "convince untruthfully".