Jax is supposed to be tied to void, I'm pretty sure the reason he looks like that is due to void energy's mutation on him similar to the Rift Herald. Darkin is not a part of his business.
It's also fairly obvious that the lamp is just for show, it doesn't really matter what he actually uses for combat. Because we can see that his power is entirely innate on Jax and not from the weapon: He charges the weapon with magic energy and bash people with it as either an active or passive, his reflex that allows him to attack fast and faster at each strike and to leap as well as to dodge are also natural abilities, and his resistance/shield is also from himself. And nothing on him has anything in association with darkness, blood or corruption etc, they are all as straightforward and "normal" as it gets. Hence it's not likely that Jax is the lamp post.
He may be related to Darkin given that he seems to have lived for a long time (I mean, isn't he from a lost civilisation that went down? How long has he lived?), so he probably had come across them at some stage possibly, but I wouldn't think it's plausible to tie him with Darkin when he still has unfinished stuff to attend to, let alone having him being a Darkin.
Not to mention if that's the case, his iconic "Imagine if I had a real weapon" would be completely lost. Not too cool.
: I am the real weapon
