Download
LockDown Browser's download website shows the download option based on your OS. Since it does not support Linux, it does not let you download it. So, to download this shitty browser, you need to change the OS in your User Agent to Windows.
After you download it, DO NOT change the name of the file. LockDown Browser uses the file as an ID for the browser. It will not work if you change it to a non-valid ID.
Install
Wine
This is a solution for running LockDown browser with Wine, provided by caleb.
This solution requires winetricks
winetricks msftedit allfonts