There are several possible issues here and it is always difficult sorting out printing problems as they can involve a chain of services extending well beyond LO. The first thing I would look at is your character encoding / locale on the Xerox workstation. It should be UTF-8 to handle the Greek characters. The left-hand example in your graphic appears to be a character encoding issue to me. Either LO or Ubuntu is not sending the correct information to the printer driver or the printer driver is not correctly interpreting what is being sent.
The second thing I would look at is the printer driver. It is always a good idea to test different drivers / protocols (as suggested by @mahfiaz). I have a HP LaerJet managed by CUPS v1.5.3, using a HP Postscript driver (which is marked as “recommended”), and accessed via Internet Printing Protocol (IPP). I find this a very stable combination. I am not clear what you mean by “Generic PCL 5e Printer” - it sounds like a driver/protocol (PCL) reference, but then you mention Gutenprint. I do not have the printer-driver-gutenprint
package installed here.
The third thing to look at is the particular character combinations being employed, especially some of the diacritics. The center and right-hand examples in your graphic show a problem with character interpretation for what appear to be the Greek dasia (U+1FFE) and Greek psili (U+1FEF). I explain in further detail in an example (rename ODT to ZIP and extract contents) as to what these may be. I have no problem printing (under v4.0.3.3) from either the ODT or PDF and the example contains text set in both Linux Libertine G and FreeSerif. I do not think the fonts are an issue.
If you could upload an example file containing some ancient Greek (e.g., from here or here) it may help further. As a guess I would say your problem is most likely to be a printer driver / protocol or locale one.