@Kzer-Za
The following should work for you; however, a small disclaimer that this is mostly from memory. 
Well, if I’m understanding your request, you wish to have two Firefox profiles, and load each of them with it’s own .desktop file – yes, this is possible.
Each .desktop file should have a different filename – a different icon is optional – and each should point to a different Firefox profile.
1. Create your two Firefox profiles – for the sake of convenience, let’s call them profile1 and profile2 – but, they can be anything you choose.
To learn how to create Firefox profiles, please see:
The Mozilla article is a little dated, but still indicates what is needed. Note that the location in which Firefox profiles are stored has recently changed and could be in either of two locations …
Profile Location(s):
- (Old)
~/.mozilla/firefox
- (New)
~/.config/mozilla/firefox
I suggest leaving the default Firefox profile alone, and creating two others.
2. Create two custom .desktop files – you can start by copying the /usr/share/applications/firefox.desktop to your Desktop folder – rename each of them as shown below.
Again, these are examples, but there is very little to change; open each in turn with your favourite text editor, and make the following changes:
firefox-profile1.desktop:
Exec=/usr/lib/firefox/firefox -P profile1 %u
Icon=firefox
Name=Firefox (Profile1)
firefox-profile2.desktop:
Exec=/usr/lib/firefox/firefox -P profile2 %u
Icon=firefox
Name=Firefox (Profile2)
Icons: Unless one is particularly obsessed with icons, the naming of each .desktop should be enough to differentiate between the two, otherwise, include the path to a custom icon after Icon=.
Example:
~/.local/share/icons/myfirefox1.png
~/.local/share/icons/myfirefox2.png
You might find Firefox icons to your liking here:
Note: The reason for creating two separately .desktop files (with different filenames) is to allow each of them to be automatically discovered and listed in the Application Menu.
Both .desktop files can be placed in either of:
/usr/share/applications/
~/.local/share/applications/
- Remember to make them executable.
I hope this was helpful.
Regards.