Cortana in Windows 10 has more user prompts with some of the latest Windows 10 updates.  To change Cortana’s lock screen settings, click the Start Button and then click the Settings gear icon, then select Personalization:

Under Lock Screen, set “Get fun facts, tips and more from Windows and Cortana on your lock screen” to Off.

Then select Cortana Lock Screen settings.  Set “Let Cortana pipe up from time to time with thoughts, greetings and notifications in the Search box” to Off.

To turn off suggestions on the Windows 10 Start menu, select Settings >> Personalization >> Start.   Set “Occasionally show suggestions in Start” to Off.