This is interesting, both because the question is new and both people who answered before me assumed that the communicators were humans or nearly human.

I think the first messages sent between organisms probably arose soon after organisms began interacting, either adversarially or cooperatively. Predation is older cooperation so I guess the first message would have been something along the lines of, "I'm about to try to eat you." It would have been communicated through the action of hunting, as soon as the hunted was able to perceive the predator.

As for the first lie, maybe that would be something like camouflage or deceptive body language. "I'm bigger than you," communicated by features designed to inflate an organism's size, or "I'm not really here," or "I'm poisonous," according to various methods of mimicry or crypsis.

Ok, these may be lame, but here is my shot at them.

1. First conversation..."No dumb ass I told you to hit the sabre toothed tiger over the head, not ME!"

2. First lie ever told..."I love you"

Caveman looks at cave-woman and asked, "How long have you had PMS?"

Immediately after this the first lie was told, "Your ass looks great in mammoth hair."

The first communicated message?

"Can you understand me? Testing. Testing. What about now?"

The first lie ever told?

"Me? Draw animal porn on the cave walls? Of course not!"

Here's what I came up with:

First message: Get out of my way

First lie: I'm not interested in you