Shortly after I began this page, I discovered to my delight that there is a place traditionally held to be the site of St. Lydia's baptism. The spot itself is preserved near a shrine to St. Peter. Not too far from the spot is a church dedicated to St. Lydia. Unfortunately, I can find very little on this place. The only mentions of it so far are on travel sites. My goal then, is to find out about the site and about the Greek Orthodox church in St. Lydia's honor. I am including in this post the best picture I have found of the spot so far.
Hopefully there is some more info out there somewhere. Perhaps I will have to go and visit the site myself to fully find out what is available.