First things first - are you sure it's not the injectors? They 'tick' quite audibly.

It's doubtful it's the lifters, as they'd quieten down as the engine became warmer.

Another couple of possibilities that aren't as drastic as they sound and that's the exhaust manifold gasket, or the head gasket. The head gasket blows 'to atmosphere' through a weak point in the gasket design. You'll loose no oil, nor water, but will be losing a small amount of compression (so power) from one cylinder. They can go on for thousands of miles like it without issue. The exhaust manifolds can also leak, although they too tend to be worse when cold.