A LED module is disclosed comprising a LED chip including at least one LED arranged to direct a luminous output centered about an optical axis towards a light exit surface; an optical layer separated from the light exit surface by a spacing region having a lower refractive index than the optical layer and a material comprising the light exit surface, the optical layer being arranged to redirect the luminous output in a direction under a non-zero angle with the optical axis; and a collimating element over the optical layer, the collimating element being arranged to collimate the redirected luminous output in said direction. A lighting module including one or more of such LED modules is also disclosed.