Can I play Lost Blender if there are no cards left in my deck to draw from?
Yes, you can. Putting cards into the Lost Zone is the main effect, so you can use this even if you have no cards in your deck. However, you cannot play it unless you can put 2 cards from your hand in the Lost Zone.
Source: TPCi Rules Team (2019-01-03), TPCi Rules Team (2019-03-21)
Can I play Lost Blender if I only have one card in my hand to put into the Lost Zone?
No, you cannot play Lost Blender unless you put 2 cards from your hand in the Lost Zone.
Source: TPCi Rules Team (2019-01-03)