Wouldn't loneliness require the whole missing company aspect? Mihawk pretty clearly doesn't like company. Just because he's alone doesn't make him lonely and as far as we've seen nothing hints that he's lonely or craves interaction with others which is kind of the definition of lonely. Robin and Brook were two of the loneliest people but since joining SH's they're not lonely anymore. Mihawk doesn't seem to want or miss anybody. The loneliest person may be that guy stuck in a treasure chest. (that's the guy, mentioned above me)But she isn't the loneliest character anymore. It doesn't take away from that fact, but that fact doesn't apply anymore because Mihawk fits the criteria better than her at this point.