The Death Star is the size of a small moon. Endor being a moon (not sure if it's small or not) has a rich atmosphere.
Could the Death Star hold a nitrogen/oxygen based atmosphere with its gravity?
(Now re-reading my question, I suppose this sounds a lot like the plot of SpaceBalls... that was not my intention)
Answer
According to various sources including the fun, but alas non-canon Death Star Technical Companion and the Star Wars: A New Hope Junior Novelisation, the radius of the Death Star was somewhere between 120km and 160km. The outer frame was comprised of quadanium steel and the interior was a mixture of quadanium steel and other metals.
Assuming the interior is completely solid metal (which it isn't) and presuming quadanium steel is similar in density to normal steel (which we don't know) then we can calculate that the Death Star has a maximum apparent gravity of around 0.04% of Earth normal.
This would be well below the point that any celestial body could retain a breathable oxygen/nitrogen atmosphere. There simply wouldn't be sufficient gravity to hold it in place.
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