You can do it using project permission scheme. You can set the following permissions there:
1. Assign issues - Permission to assign issues to users. Also allows autocompletion of users in the Assign Issue dropdown.
According to your case you have to set the permission only for the Project Lead
2. Assignable user - Permission to be assigned issues. (Note that this does not include the ability to assign issues
You have to set this persmission for the Project Lead and admin user (if admin user is a role or a group you can set this permission for a role and a group as well )
You can read here about project permissions
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