First of all, it's a great question!
The Torah (that is the five books of Moses), simply says that you should eat the meal in great haste. The translation from Artscroll reads: "So shall you eat it: your loins girded, your shoes on your feet, and your staff in your hand; you shall eat it in haste - it is a pesach-offering to Hashem."
The word in question is "Chipazon" which means haste. It is a unique word that doesn't appear too often.
There is no indication in the text that first Passover, they did not eat lying down. Their last meal was eaten quickly. You can certainly eat quickly and be sitting/lying. The definition here is simply that they ate quickly, gathered all their possessions together and left.
This is the first Passover, there is another Passover mentioned in the Torah - how they celebrated afterwards. If you look at Deuteronomy 16:1-8, you will see outlined there is a fulfillment of how to celebrate Pesach, post-Exodus. To achieve the fact the Jews left in haste, we eat unleavened bread (commonly referred to as Matzos), because we left in haste. (Deut 16:3).
Jews, since the first Exodus from Egypt have been celebrating Passover meal by eating unleavened bread (Matzos) as a way of expressing that we left in haste, just as the Torah tells us in Deuteronomy 16:3. The verse in Exodus 12:11, tells us that G-d Himself told the people at the time of the Exodus to gird their loins, don sandals and eat quickly in haste because they're going to leave that night.