I actually don't think he's lying about dying. I think he allowed himself to die (calling off medical treatment, etc) to enter the spirit world and will find a way back. We've seen many times that trolls and their loas are capable of crazy stuff including reincarnation or bringing people back from near-death.
I agree that he wouldn't lie to us or the Horde. I kinda of agree with the above post. There's a line of dialog about him meeting with an "old friend" and I think it's extremely telling. Vol'jin has or had some kind of plan, and it makes sense considering Blizzard clearly wants to push him as the next Warchief and needs to give the playerbase a reason to really respect him.
His entire occupation/class/job whatever of shadow hunter basically says that he communes with spirits and works with the troll loa aspect of death, Bwonsamdi. It's all set up way too well. And that's another pretty big point that I never thought about, honestly: if Vol'jin was gone for good, you can be almost certain they'd pull a Saurfang of sorts and have someone rise up as the new troll leader. That's conspicuously missing, considering it's happened so far every single time a racial leader has died.
But yeah, Varian is dead. Mega dead. There's no way that guy is coming back, they've made too big of a deal out of it at this point compared to how Vol'jin just kinda unceremoniously got thrown on the death bus and everyone immediately moved on.