I saw one of these lenticular cards somewhere, so I started nosing around the internet for some examples. When you look at it from the left you see one picture, from the right you see another.
Found out they are called "flippix" in the UK. Started checking out the links and next thing I knew I had a something shiny moment because FlipPix means a whole other thing in the USA. Off on a tangent! See the US FlipPix in action here. You can buy printable blanks to make these, but the finished size is quite small. Then I remembered I had a sample of this in my idea file already--from a Carol Duvall book. (You can see hers online, too, here.)
I ended up making my own with CorelDraw. I wanted it bigger than the template you can download to use with the premade sheets, and smaller than the Carol Duvall sample. It also allowed me to print the pictures directly onto the card instead of cutting and pasting.
Flipping the panels to the top and bottom returns to the first picture.