When using InPrivate Browsing mode in Internet Explorer, I do not see the LastPass extension. Why?
InPrivate Browsing helps prevent Internet Explorer from storing data about your browsing session. This includes cookies, temporary Internet files, history, and other data. Toolbars and extensions are disabled by default.
You will need to disable this feature: View > Toolbars > and disable the option for 'Disable toolbars and extensions when InPrivate browsing starts', re-start the InPrivate browser and you should now see the LastPass extension icon.