Try this in Post Lister code:

:VAR(USER_ROLE).IFMATCH(Admin).THEN.VALUE(true).SET(can_edit).NULL.ELSE.NULL;
:VAR(USER_NAME).IFEQ.VALUE(%username%).THEN.VALUE(true).SET(can_edit).NULL.ELSE.NULL;

:VAR(can_edit).IFEQ(true).THEN(<a href="/delete-post">Delete</a> | <a href="/edit-post/%id%/%title%">Edit article</a>).ELSE.NULL;

It will allow only Admins and the user who created the post to edit or delete it.