So this is more a feature how (and where) the example projects manager is implemented at Lazarus project? Assuming "\share\" in linux/unix lingo means (read & execute, but NO write for mere mortals) ...?
Not quite. Let's start off by assuming that the executable files ("binaries" or "shell scripts") are in /usr/bin and /usr/local/bin, then the /usr/share and /usr/local/share directories are broadly there for the corresponding non-executable files.
Your distro (I think you said you're using Ubuntu, I use Debian which is related) will install binaries from packages (.apt etc.) in /usr/bin and /usr/share. As an aside, some non-Linux unices would put stuff which was optional rather than essential in /usr/opt/bin and /usr/opt/share, and some Berkeley derivatives would use /usr/ucb/bin and /usr/ucb/share... I think you probably get the idea. There's also sometimes binary libraries (i.e. not executable in their own right) put in /usr/lib, /usr/local/lib and so on.
If you build something locally, it's generally good practice to put it in /usr/local with executables in ...bin, library files in ...lib, supporting data in ...share and so on. If it were from a third-party archive and had a complex history starting off with SunOS/Solaris or one of the Berkeleys then it might go in /usr/opt or /usr/ucb, but hopefully by now you get the idea.
The twist here is that even if you put the executable for the main Lazarus IDE in /usr/local/bin, on occasion it wants to rebuild itself e.g. if a support package is added. So for that reason alone it's better practice to have a symlink (qv) or shell script in /usr/local/bin, which transfers control to the IDE binary elsewhere. In addition, there's a great deal of stuff associated with the IDE (loosely speaking, resources) which naturally fits into /usr/local/share (although as I said, I use /usr/local/share.lazarus to keep my standard /usr/share uncluttered).
Each user will have configuration and state files in (by default) ~/.lazarus, where ~ is shorthand for the name of his home directory. But you don't necessarily want each individual user to be able to update and rebuild the IDE: it's better to either designate one user who is then the owner of the entire /usr/local/share/lazarus (or, in my case, /usr/local/share.lazarus/...) tree, or to allow it to be done by any member of a trusted group (i.e. "staff" in my earlier example).
But going back to your original question: an example program being tinkered with is very much the domain of one specific user, so should generally be copied out of /usr/local/lazarus etc. into that user's working area.
Bit rambling, I'm afraid, but hopefully answers whatever it was you asked :-)
MarkMLl