I saw a really nice discussion regarding the minhag to wish L'chaim over wine in Alei Tamar to Brachos 6:8. He discusses the three Tannaitic sources that refer to the minhag and the many intricate details on the correct way to wish L'chaim.
There are several creative explanations on the reason for the custom.
The Avudraham and Daas Z'keinim to Emor explain that this is based on the opinion that the forbidden fruit that brought death into the world was a grape. Therefore, when drinking wine one says L'chaim to counteract this effect. Also, because one who was sentenced to death was first given wine in order to confuse him. Therefore, wine is symbolic of death.
Another possible explanation (I don't have any source for this) is on the custom I have seen of having wine to separate between fish and meat courses as having the two together is considered dangerous. The L'chaim can refer to the fact that the wine counteracts this danger.
Most likely this is just another example of cultural borrowing. Wikipedia notes that:
According to various apocryphal stories, the custom of touching glasses evolved from concerns about poisoning. By one account, clinking glasses together would cause each drink to spill over into the others (though there is no real evidence for such an origin) According to other stories, the word 'toast' became associated with the custom in the 17th century, based on a custom of flavoring drinks with spiced toast. The word originally referred to the lady in whose honor the drink was proposed, her name being seen as figuratively flavoring the drink. The International Handbook on Alcohol and Culture says toasting "is probably a secular vestige of ancient sacrificial libations in which a sacred liquid was offered to the gods: blood or wine in exchange for a wish, a prayer summarized in the words ‘long life!’ or ‘to your health!’”
In regards to the last reason offered. In a recent trip to the Met, I saw the following vessel which contains the
Although, it might seem strange that a Hellenistic pagan custom should have entered the Jewish canon. we do know of cases where this has happened. See S. Lieberman Hellenism in Jewish Palestine for examples.
Re: the question of cultural borrowing, I recently noticed the parallel between the Japanese tale of Urashima Taro, and the Talmudic story of Choni HaMaagel (See here) although it is highly unlikely that either culture had any contact with each other.