You do not need to manually uninstall the game because if you do you will lose your saves you just need to need to update the base APK.
All Ren'Py game saves on Android are stored in "Internal Storage/Android/data/[internal packagename]" the internal packagename is the used when compiling the APK.
Here're images to show the location of Lust Odyssey's saves:
Open your file manager and then open the folder labeled "Android" 
Open "Data" 
Open "Files" 
Use your file manager find tool to lo locate the folder "lusty.odyssey" 
Your saves should be in this folder
Itch used to have a mobile client but Itch's lead devoloper abandoned it as he was busy with the desktop version. Since the source code for versions of the Itch client is hosted on GitHub, a developer named gardenapple created a new mobile client called Mitch that converts Itch's website into a standalone app which will notify you when there's when you log in and download the game using the app. I'm writing the comment by using Mitch:
