I ran into something like this once for an app that was installed via GetJar (for free) and I later wanted to install it via the Play Store. I think the following might work:
- Open the app page in the Play Store in Chrome on your desktop. If you don't have/use Chrome, other browsers probably have similar functionality, but I can't tell you exactly how to do it in anything other than Chrome.
- Right-click on the Installed button near the top of the app listing and select "Inspect Element"
- A few lines above the highlighted line in the element inspector you should see something that says data-ispurchased="true". Double-click on true and change it to false and hit enter.
- Close the element inspector and click on the same Installed button that you right-clicked on earlier. It should proceed as if it's not currently installed on your device.