I think that you're correct in assuming that the great lie was one that developed over time. In all likelihood, the charade started simple, using half-truths and whole truths to unify Ishgard against Nidhogg and his horde. The original four knights most likely did not try to convince everyone that their beloved friend dragons were secretly evil and plotting to kill them. The original lie was likely simple, and based MOSTLY in truth: That Nidhogg wanted to kill them all, and had a horde of loyal followers to carry out that wish. However sympathetic some dragons might be, there were enough adversarial that war was inevitable, and the humans needed to band together for their own protection. In the early days of the war, it's even possible that some dragons allied WITH their human friends, maybe even with the full blessing of the Knights Four.

The problem is, though, that half-truths and whole truths were not enough. After a century or so of war, with no end in sight, it's little surprise that the Ishgardians would have begun to tire of it and yearn for the days of cooperation between the races in the past. Folks would begin to question the government, start calling for overtures of peace. The folks in charge know that peace would never be possible, due to their inside knowledge of Nidhogg's motivations, and all this anti-war rallying was tearing Ishgard apart. So, they started a long-term campaign to change the history books: The anti-war protesters are ruthlessly silenced, and the government starts taking steps to stymie such uprisings in the future by rewriting history to paint dragons as a whole in a negative light. There is no hope for peace with the dragons, so don't even try to find allies among them. All dragons are our enemies. Rumors of long-ago friendship are lies, perpetuated by the dragons to bring dischord. All who consort with dragons are heretics, and must be purged.

While it might seem illogical to try to hide the fact that the two races were once allied, in the face of blatant evidence as close by as the Dravanian Forelands, the leaders saw it as necessary in order to keep Ishgard constantly united against a foe that they knew would exploit any lack of solidarity on their part. After centuries passed, things that were common knowledge became folklore and myth as their leaders relentlessly ground the lies deep into the public's consciousness. A thousand years is a very long time, after all, and the Ishgardian leaders knew they'd be playing the long game with Nidhogg if they were to win at all.

Of course, the idea that history can be so easily changed is based on the arrogance and cynicism of powerful, yet flawed leaders. There have been many throughout history who believed they could change history simply by flexing their political muscles - Stalin being one notorious example. I don't think anyone here seriously believes that Ishgard's policy of writing draconic friendship out of the history books was a viable plan, or the correct thing to do - but it's certainly possible that the lords of Ishgard were convinced that it was.