Go into the document settings and under custom class options, add the word 'english'. See below:

This adds English support to the document (currently only Greek was listed). You can see the actual TeX code by going to View --> View Source
. You will see that adding English to the custom class options modifies the first line like so (also including the next two lines for next point):
\documentclass[12pt,a4paper,greek,english]{moderncv}
\usepackage[T1]{fontenc}
\usepackage[iso-8859-7]{inputenc}
The problem is that you typed your document in English and this will no longer accept Greek character support (it doesn't look like you have any actual Greek anyways, though - it is just English so far). If you need Greek language support, I recommend using XeLaTeX as it supports Unicode (assuming you know how to type Greek on your keyboard), and changing the settings in the Language section of the document settings rather than modifying the class. You may need to change the font and other settings to use Unicode support in LyX, and you may have some additional issues as well (I just write TeX directly for Greek documents, I don't use LyX).
It seems from my research (I'm not very experienced with LyX) that using the babel
package and specifying when you write in Greek may be best (unless everything except the email should be in Greek, then do vice versa - although it appears that nothing is in Greek thus far). To do this:
- Document --> Settings --> Language to Greek
- under Tools --> Preferences --> Language Package
- Change to
\usepackage[english,greek]{babel}
You will have to insert the following code everytime you alter the language
\selectlanguage{greek} or \selectlanguage{english}
This is not the optimal way to handle this but from reading forums it seems other routes are somewhat buggy in LyX. See also How to encoding of Lyx LaTeX output without Lyx adding inputenc declaration to preamble
See also fontenc vs inputenc
babel
,inputenc
,fontspec
, etc. A MWE will help tremendously.