Wikipedia has the history:
https://en.wikipedia.org/wiki/Giclée
It's really just a bit of artspeak jargon, so that galleries and dealers don't have to say anything as crass as 'inkjet' (see also 'gelatin silver print' for conventional black and white print, or 'C Type print' for chromogenic colour). It's implied that high quality materials have been used, though there's no fixed definition.
A LightJet is very different; it's a specific brand of printer that exposes conventional light-sensitive paper (or film) using a laser; the latent image is then developed chemically as usual. This technology can be used to make large, high quality prints.