Thank you for your message. We do have users using the LG Stylo and have downloaded the Gateway app, please use the information below, which was given to us by Google Play for people with this issue.
Make sure you have an Internet or mobile data connection. Then, restart your device.
Update the date and time on your device.
Remount SD card:
Touch Menu > Settings > Storage > Unmount SD Card to disable the device's memory card.
Remove the SD card from the Android device. Wait a few seconds, then re-insert the SD card.
Disable the installation of apps with unknown sources:
Navigate to Settings.
Under the Personal header, touch Security.
Scroll down to Unknown sources and make sure that the slider to the right is off(grey).
Clear cache for Google Play Services app (Go to Settings > Apps or Application Manager > ALL > Google Play Services > Clear cache > OK).
Clear cache data for the Google Play Store app.
Uninstall and reinstall the Play Store updates. (Go to Settings > Apps or Application Manager > Google Play Store app > Uninstall Updates > OK). As long as you have a strong Internet connection (Wi-Fi or mobile data), your Play Store app will update to the latest version within a few minutes.
As the problem appears on Games, uninstall the Play Games updates. (Go to Settings > Apps or Application Manager > Google Play Games app > Uninstall Updates > OK).
Install system updates. To do so, try the steps listed below:
Open your device's main Settings app.
Select About or System updates (depending on your device, this may be different).
If an update is available, follow the on-screen instructions to install it on your device.
Try installing again.
Make sure Download Manager is turned on.
Check your device's available storage.