The large transient current in a lightning strike generates a similarly large and transient magnetic field that can induce currents in nearby conductive mediums (like human body tissues), even if they're electrically isolated from the strike. A Faraday cage provides protection against both the direct electrical current and the EMP from a strike, but the degree to which it protects the interior of the cage from the EMP depends on the thickness and skin depth of the conductor used and the size of any gaps in the cage relative to the wavelength of the EMP.
