Can I use Lunar Boon without hand cards?

Yes, you can play Lunar Boon even if you have no cards in your hand.

According to the rules regarding discarding and the "Do as much as you can" (DAMAYC) principle (Rule 8870), if an effect instructs you to discard but your hand is empty, you simply discard zero cards and continue with the rest of the effect. Because the discard is not listed as a cost (it does not use "to" or "in order to" phrasing, and it is part of the effect resolution), you are permitted to play the spell even if you cannot discard a card.

You will successfully discard zero cards and then proceed to draw two cards.