"Could not add write permission to the file because you do not own it"
This means that the project was created by a different user. Log as that user, or if you cannot, create a "test.txt" file next to the file you can't unlock.
Open Terminal, go to the folder where the project resides, and run a command such as
ls -la test.txt project.pbxproj
You should see a list such as:
-rw-rw-r-- 1 dakkar users 434 Nov 23 12:17 project.pbxproj
-rw-r--r-- 1 lserni users 1 Nov 25 00:14 test.txt
Now, the "-rw-r--r--" is the permission. You just created test.txt, so those are the correct permissions from the GUI. r counts for 4, w counts for 2, x counts for one; rw-r--r-- is therefore 6,4,4. In the example, project.pbxproj is 6,6,4.
So the two commands you need are
sudo chown lserni:users project.pbxproj # To set ownership
sudo chmod 644 project.pbxproj # To set permissions
If you are in the project directory and are absolutely, utterly, deadly sure that nothing there or in its subdirectories should belong to anyone but you, then you can mass-change ownership of the directory, its subdirectories and all they contain:
sudo chown lserni:users -R .
If you do the above in the wrong directory (not yours, not a project directory, etc.), the -R (recursive) flag is a recipe for disaster, so be careful.
Just in case, remember that directories must have all x's set, so what is 644 for a file would become 755 for a directory.
When finished, you can delete the example file 'test.txt' - actually you can do that as soon as you have written down what the correct ownership and permissions should be.