The corner I'm referring to, where the yellow and red lines meet in this image (basically where the hinge for the chest would be) is where the lid is pivoting from, the point around which it is rotating. So this would serve as the center of the ellipse.

This is why your own diagram (this one) is a correct start (at least at step 1), because it places the ellipse's center in the correct place.

The only thing to keep in mind is that when placing this ellipse, you need to make sure that the properties we explored in the cylinder challenge, about how to draw an ellipse that actually represents a circle in 3D space, are holding true. That is, ensuring that the minor axis goes towards one vanishing point, and the lines defined by your contact points go towards the other vanishing points.

What you have drawn there in step 2 is an adequate approximation, but it is technically not correct because it does not meet the criteria for an ellipse that represents a circle in 3D space. That said, even though it's not correct, for the purposes of positioning the lid, it is close enough. So it's up to you if you want to go for close enough, or 100% accurate.