We have analyzed and compared distance dependences of electric and magnetic fields due to a lightning strike to a tall object and due to the same lightning strike to flat ground. In both cases, lightning was represented by a transmission line energized by a lumped voltage source connected at the channel attachment point. The resultant total charge transfer to ground was the same regardless of the presence of strike object. The electric field for the strike-object case is reduced relative to the flat-ground case at closer distances from the object. If we assume, in an idealized case, that the return stroke wave front speed is equal to the speed of light, v = c, the current reflection coefficient at the bottom of the strike object ρbot = 1 (grounding impedance Zgr = 0), and that at the top of the object for upward-propagating waves ρtop = 0 (characteristic impedance of the object is equal to that of the channel Zob = Zch), the ratio of the vertical electric fields on ground for the strike-object and flat-ground cases (electric field attenuation factor) will be d/√(d2 + h2), where h is the height of the strike object and d is the horizontal distance from the object. The corresponding ratio for the azimuthal magnetic field is equal to unity. We show that the ratio for either electric or magnetic field increases with decreasing ρbot (ρbot < 1), decreasing ρtop (ρtop < 0 except for the case of ρbot = 0), and decreasing v (v < c), and at larger distances can become greater than unity. We additionally show that the ratio of the far fields for the strike-object and flat-ground cases is given by (1 - ρtop) (c/v + 1)/(1 + ρgr), where ρgr is the current reflection coefficient at the lightning channel base when the channel terminates directly on ground. For realistic values of ρtop = -0.5, ρgr = 1, and v = 0.5c, this ratio (far field enhancement factor) is equal to 2.3.