The earliest I know of the tradition is in augury. Roman augurs and Greek augurs faced in opposite directions when observing the signs, so that a sign in the same place would appear on opposite hands. The east in both Roman and Greek augury was the propitious side of the sky, and the west was the opposite--to a Greek, facing north, signs in the favorable east were on his right, but for a Roman, facing south, they were on his left. From a very early date it appears that the Romans adopted, for literature, the Greek convention that the left was the ill-omened side, even though Roman religious ritual maintained its traditional orientation. Indeed, we do find that occasionally the Roman practice is referred to, despite being less popular poetically (and even in prose). Catullus 45, for example, has a pair of lovers, Septimius and Acme. The former is a Roman, the latter a Greek--Catullus describes Love as sneezing on their left side after Septimius speaks, and then sneezing on their right side after Acme speaks, to pound in how much in love they are. This is rather rare though, outside of a religious context (and here I think you could argue that there is a religious context, since Catullus is describing the blessing and will of Amor), and usually when sinister in Latin literature is supposed to have any connotation of good or bad omens it means the latter rather than the former.