According to Rhett Allain all you need is two trillion kilograms of lego. That weighs as much as 400 million elephants. Can you imagine trying to launch 400 million elephants into space? In low Earth orbit (~300 km), the scale model Death Star would appear bigger than the moon from earth:

People would mistake it for a moon, just like Han Solo did. Well, it look just like the moon except that it would just take a couple of minutes to pass across the sky where the moon doesn’t really seem to change its position.

Check out the figure that Rhett put together comparing the scale model to the World's tallest buildings.