Fun responses here.
So I got a couple off-the-beaten-path suggestions, just to mix it up a bit.
As I recall we never find out the mirror's origin, so we have no idea how powerful it truly is. I mean, seeing someone's deepest wish is generally treated as a fairly common skill among mages and telepaths.
So I will submit that Diana, as an avatar/god of Truth, would be immune to the "lies" the mirror tells.
And I submit that Batman, at least in his common post-DKR form, can't actually be happy and would see a jumbling mess of conflicting, distorted images as the enchantment on the mirror tries to dig through his pile of emotional baggage and psychosis. But that's just the more extreme, modern age version of Bats, keep in mind.
And Superman, as a being who compartmentalizes his life to an extreme degree, would actually see two separate images. One in which Krypton is alive and well, and one where he is with Lois and Jon and hung up the cape because the world no longer needs a Superman to protect it. Or, if not that, then a sustainable, permanent version of New Krypton where both of Clark's cultures combine and he no longer has to divide his life.
And Lobo would just see a beer bottle that never gets empty.