Okay.. First off I'm going to start off with why Chibiusa became Black Lady..
She felt like everything she did just wasn't worth the effort that she put into it. All the saving people just didn't seem like it was really helping anyone. She also felt like she was being ignored and unnoticed. She felt like it was also her fault for feeling that way because it wasn't anything that Usa did. Just with all the change in her life she felt left out and almost unloved. She thought the only one that paid any attention to her was Mamoru and he turn out to be a real jerk when he was needed the most. Her whole life as she knew it was falling apart and turning upside-down. She just wanted some order in her life so she did the only thing she could do to find it... She left. When she teleported she ended up on the old ruins of the old moon kingdom. The extra negative energy got to her and because of all the doubt she was feeling it changed her.
Now on to why she made Lunar...
She was afraid that after Usa found out what happened she would come looking for Chibiusa and instead find Black Lady so she started to think of a way to protect her from the Ginzuishou because she knew that as soon as Usa came with that she wouldn't stand a chance just like before. She also was getting very lonely on the ruins of the moon and thought a companion would do her some good. So she finally came up with a plan on how to protect her from Usa and would also serve as a companion. Which is where Lunar comes in.
Now on how Lunar was made..
After thinking of what type of companion and protector, Black Lady used a black kitten from planet Earth and exposed it to large amounts of Crystal Moon and Dark Moon energies that changed and transformed the kitten. After the change, the kitten takes a form of a young man that is a mage of both elements. Black Lady named him Lunar Eclipse and he is her personal guardian and companion as well someone she sometimes ask for wisdom.