I recently installed the Arduino IDE on an Raspberry Pi 3B running the April, 2019 version of Raspbian Stretch. I do not see the Library Manager in the drop down menu. I've tried installing from the terminal as well as from the browser. There doesn't appear to be any forum info to support this issue.
When you install the Arduino IDE via apt install arduino, you get an extremely outdated and possibly modified version of the Arduino IDE. This version came before some very useful features like Library Manager were added. Please always use the official version of the Arduino IDE downloaded from the downloads page:
For the Raspberry Pi, you want the "Linux ARM 32 bits" download.