Lucid dreams have little difference from normal dreams when it comes to memories of them after you wake up. They WILL feel hazy and if you are not well trained in dream recall you may forget them all together. This is a safety mechanism which you'd better keep and not breaking it. Mixing real life memories with dream memories can be disastrous. It CAN happen but the effect usually fades after a few hours.

In terms of memories after waking up, lucid dream is different from normal dreams in one aspect. You do remember your intentions and other abstract thoughts clearly. It's simply because the corresponding brain regions, such as those responsible for reasoning and self-reflection, are activated during lucid dreams.