1. Here's why

Sun shadows are only shown if the Editor Quality is set to 2, 3 or 4 star Editor Quality:

• F4 and 4 star Editor Quality: Highest quality level.
• F3 and 3 star Editor Quality: Low-quality terrain and terrain self-shadows off.
• F2 and 2 star Editor Quality: OmniShadows off.
• F1 and 1 star Editor Quality: Sun and Spotlight shadows off and some movie effects off.

1.1: Press the F2, F3 or F4 key - or click on the 2, 3 or 4 star buttons on the Settings screen - to display sun shadows: 

See also:

Knowledge Base: Is there a list of all the keyboard shortcuts in Lumion?

Knowledge Base: Why are Spotlights not casting shadows?