There are two methods. Both examples add the home icons from the Elegant Theme Font. See here fore other icons.

Method 1

Source: https://joshhall.co/how-to-replace-text-with-an-icon-in-the-divi-menu/

1. Copy the icon Unicode from the Elegant Theme Font into the navigation label of the menu item.
   • Dark Home icon: 
   • Light Home icon: 
2. Add CSS Class to the menu item: menu-home
3. Add the following CSS (font size and color are optional)

More icons

• https://www.elegantthemes.com/blog/resources/elegant-icon-font (Elegant Theme font (ETmodules)
• http://graphemica.com/ (unicode, remove the font-family from the css)
• http://www.fileformat.info/info/unicode/category/So/list.htm (unicode, remove the font-family from the css)

/* -- START Menu Icon -- */
.menu-home a {
    font-family: 'ETmodules';
    font-size: 18px!important;
    color: white!important;
}
.menu-home a:hover {
    color: #8dc63f !important;
}
/* -- END Menu Icon -- */
Code language: CSS (css)

Method 2

Source: https://divi.space/divi-tutorials/divi-menu-icons-without-plugins-or-font-awesome

1. In the WordPress menu, enable the CSS classes in the screen options. Then open a menu item and enter one of the classes in the CSS classes field like:
   • menu-icons menu-icon-home-dark
   • menu-icons menu-icon-home-light
2. This adds the icon in front of the text of the navigational label. If you don’t want to replace the ‘Home’ text with the icon, replace the text with <wbr> (invisible no hyphen break) or &nbsp; (no break space). A normal space doesn’t work.
3. Add the following CSS :

/* -- START Menu Icons -- */
.menu-icons a { padding-left: 10px; } 
.menu-icons a:before { font-family: 'ETmodules'; position: absolute; } 

#main-header .menu-icons a:before { top: 0; left: 0;} 
#mobile_menu .menu-icons a:before { position: relative; }
.sub-menu .menu-icons a:before { margin-top: 6px; left: 0; } 
#top-header .menu-icons a:before { left: 0; top: 0; }

.menu-icon-home-dark a:before { content: "\e074"; }
.menu-icon-home-light a:before { content: "\e009"; }
/* -- END Menu Icons -- */
Code language: CSS (css)