Technically speaking in Latin sinister maintained its favorable meaning throughout antiquity. At least in some usages. The favorable or unfavorable quality of the right and left hands derives, at least in our texts, from the practice of augury, although I'd be surprised if there wasn't simply some folk-tradition underlying it in reality. In both Greek and Roman augury the well-omened side was the east, facing the rising sun. Greek augurs faced north, so the east was on their right, while Roman augurs faced south even after contact with the Greeks, so the east was on their left. Religiously this never changed, and with reference to augury sinistra is consistently used to mean well-omened, except when referring to Greek practice. Lewis and Short state that the unfavorable aspect of sinister is something of the post-Augustan writers and that it's a poetic usage originally (probably due to the frequent Hellenization present in Latin verse), but I can't think of anyone before Cicero who uses the word as a favorable or unfavorable indicator outside of augury at all, so it may just be a lack of material the leads them to that conclusion