gTimeJohnny!

The connection here is not between lucidity and realism but rather between awareness and vividness. The more you're aware of during the dream, the more full, or vivid it seems.

More lucidity does not equal more realism. If this were the case, then non-lucid dreams could not be realistic, which isn't true. Lucid dreams can be non-realistic as well.

More vividness also does not equal more realism. For example, if a dream is vivid, unrealistic things such as dolphins flying around your house can still happen. The realism of a dream depends on what you're subconsciously expecting to happen, not on how much you're aware of.

As far as you being able to remember things better when lucid, that's a result of better internal awareness, not external awareness. External awareness makes the dream vivid, while internal awareness helps you remember things. More external awareness does not equal more internal awareness. If this were the case, then all vivid dreams would be lucid, which they aren't.