Hi,
Ok looks like the issue is solved.
For some reason there was already a folder named "tmp" in my home directory (so, at the exact same place where Lazarus was trying to save files).
The interesting detail is that the "tmp" folder was owned by root, so I (my user) actually did not have the rights to write into that.
No idea who or what created that folder -which was empty by the way-.
I re-created that folder using my regular user and boom, issue went away.
After codesigning gdb, I then managed to successfully build and run the default project.
Pfffeewww.
Thanks everybody for your insights, I can now start digging deeper into the toy and see what it's capable of.