https://grbs.library.duke.edu/article/viewFile/15275/6797 p. 147 cites it as the opening of a letter translated into English. I don't have a date on the translation, but it seems to be a bit old, as you can tell from the archaic forms.
Between the translation and the older English being used, it requires a little parsing.
"I pray": Not used much any more in this way, but equivalent to the modern "I hope" or "I wish". Pray has shifted in meaning over the years and is now only really used in idiom ("pray tell") or in a religious or legal context. However, it used to mean something similar to "petition/hope/wish" all at once.
"greet you with good fortune": The writer is hoping that the recipient has good fortune at this moment. IE, that the greeting comes "with" or at the same time as "good fortune".
The modern equivalent would be "I hope this letter finds you well." or similar.
The second phrase I can only speculate on, but two obvious interpretations leap out to me:
1) It is using "greet" differently than the first phrase. "I hope to meet you in person" along with a complement "your sweetest person". This form used to be more common. "I hope to greet your most generous person soonest" etc. So, it could be "You are very sweet and I hope to meet you in person."
2) It is simply poetic repetition, and the entire sentence condenses down to "I hope this letter finds you well, sweet person."
The problem with interpreting this is that it is a translation of Greek into older English, and done in a rather poetic style, both because the original writing was done that way, and because older translations tended to use flourish over direct meaning. However, the general meaning is fairly easy to parse.
"Greetings. I hope things are going well. (minor compliment)" and possibly "I hope to meet you in person."