Hi Alexander,
Please open an Command Prompt (admin) and start the installer manually, using msiexec.exe:
For example, if LockDownBrowser-2-1-6-02-364713981.msi is the setup file name and it's located in the C:\ drive's root, run this command:
msiexec.exe /i "C:\LockDownBrowser-2-1-6-02-364713981.msi"
If that doesn't help, check the permissions for your temporary folder. To do so, open Command Prompt admin and run these commands:
icacls c:\windows\installer
icacls "%temp%
icacls c:\windows\temp
Copy the output and post it here. You can also post a screenshot of the output window showing the output of all three commands.