Developers Rotating Canvas has developed a lens that allows you to search the Google Play Store right from the Unity desktop. Like other lenses, you just need to hit click on dash or tap the windows key and navigate to the lens to start searching. The lens shows three results and also has an option to view more results. When you click on the link, a web browser opens up taking you to the Google Play Store from where you can install the app on your Android device - yes you need to be logged in to your Google Play account.
There is not much functionality withing the lens yet beyond allowing you to search the Google Play Store from within Dash. Also you cannot group results into categories like Apps, Books or Movies.
To install this lens in your Ubuntu machine, you need to add a Launchpad PPA. To do so, type in Terminal:
sudo add-apt-repository ppa:abhshk-btra/rotatingcanvas
sudo apt-get update && sudo apt-get install googleplaylens
Once you have installed these packages restart Unity by logging out and logging in and you will find the lens in your dash.