As what? A corpse? Lambert is clearly dead by the time Inquisition takes place. It was pretty darn obvious from the end of Asunder that Cole murdered him. And how is it Weekes fault? It was Gaider who killed of Lambert.
I like Dave of Canada's idea from the past:
I'd like to imagine Lambert as being in a coma or vegetative state, being preserved and kept secret to prevent the Templar from defecting. The irony of the situation being that only magic could save him.
But beyond that, his fate was kept ambiguous. Even World of Thedas said he was "missing in action" only, rather then straight killed. I mean, really, if Cole killed him.... why was he reported missing for so many years? What, did Cole chop up Lambert's body into little pieces, throw him in acid, drop it in the ocean, and then sick an iceberg on top of it for good measure?
I can only assume the higher ranking Seekers and Templars deliberately kept that info to themselves so as to not destabilize their infrastructure.