Well, that's what it feels like. As well as all the attempts I've had at the garment, I used up a whole ball of pink acrylic trying to make a lapel that wouldn't flip up - the room was covered with little pink tongues of knitting. I wish now I'd photographed them all.
Then I emailed Rowan for advice - and good for them, they replied. Rowan suggested doing the increase by knitting into the front and the back of a stitch, and doing it two stitches from the edge. This worked better than anything I had been doing, but it still wasn't right. The lapel still wanted to flip up. Rowan also suggested adding a stitch to hold it in place - but there must be a way to get the knitting to lie flat.
Of course, Lucy Neatby knows - she draws a diagram to show how the edge stitches get stretched and 'unhappy' when you shape them. She also drops in that it's something to do with isosceles triangles, but anyway, what you have to do is 'be kind' to the edge stitches, because increasing along the bottom of the lapel means they have to stretch further - that's why they go tight. I made one lapel by using a bigger needle at the edge, which was fiddly and still a bit tight, so the second one I kept the same needle and tried to knit with loose yarn on the last 6 stitches and that seemed to help.
Now to learn Lucy's buttonhole for the other side.