Hi,
LastPass doesn't work like some password managers such as 1Password or Dashlane, that have a desktop application connected and communicating with the browser extension. LastPass only use the browser extension.
They do however provide a desktop application for filling desktop application passwords, as you can see
here, but it won't add any feature to your browser extension. They also have what they call the "LastPass Universal Windows Installer", that detects which browsers you have and install the extensions for those automatically. You can find all their extensions and applications on their
download page.
To answer your question, you should stick with the extension, as it is how LastPass is designed to work. Also their desktop app isn't very good.