Very interesting. Looks very good, my first impression is that it is better than the KHexEditor which I used so far.
The download site is
https://github.com/michalgw/mphexeditor. If you know git you know how to clone the repository, if you don't you can download a snapshot by means of the green "Clone or download" button, then "Download zip".
In order to install go to "Packages" > "Install/Uninstall packages", navigate to the folder which contains the MPHexEditor sources and load the file src/mphexeditorlaz.lpk. Click "Compile". Probably there is a compilation error because function "RenameFileUTF8" is not found in unit mphexeditorex.pas. Add unit "LazFileUtils" to the uses clause of unit mphexeditorex. Compile again - it should work now. Then click "Use" > "Install", confirm to rebuild the IDE. Recompilation of the IDE will take some time. When Lazarus restarts you find the two components, MPHexEditor and MPHexEditorEx, in the component palette under "MPHexEditor". I don't know what the "Ex" is good for (it does look rather Windows-centric although there is a conditional directive for compilation on Windows.)
For testing, I added a TMPHexEditor to a new project's main form and had it load the exe file in the OnCreate event of the form:
procedure TForm1.FormCreate(Sender: TObject);
begin
MPHexEditor1.LoadFromFile('project1.exe');
end;