I think what your looking for is the HTML Output class which allows you to create basic HTML files in Apps script.
A script such as:
function myFunction() {
var threads = GmailApp.getInboxThreads();
var messages = threads[0].getMessages()[0];
var raw = messages.getPlainBody();
return raw;
}
function doGet() {
var raw = myFunction();
return HtmlService.createHtmlOutput('<b><p>'+ raw + '</p></b>');
}
Will allow you to create a HTML file that has the content of the users last email message whenever they visit the deployed page.
My sample above is very basic, but you can tidy it up to display what you want.