The official Statement for Project Lead from the Documentation
"Project Lead - user fulfilling the role of 'lead developer'. Used as the default assignee, and potentially elsewhere in JIRA."

And all Project Permissions are regulated by the Permission Schemes. This has the bad effect that someone can be the 'Project Leader' but does not have any right to be assigned for an issue although he is the default assignee!

Usually a Project Leader has the appropriate rights to have this 'be assigned' right. But the right to Administer a Project is not that easily given, because this is called 'Administer Projects' and concerns all Projects with this Permission Scheme.

So my Workaround would be to give every User a own Permission Scheme, which i then can assign to a Project where he is Project Lead.

Maybe i am a bit wrong with my conclusion, but my understanding of a Project Lead is a bit more than just (default Assignee).

It would be nice if you can resolve this Issue