I didn't know that Overlord Lover was the name of a novel, nor did I know if there was an animation. If you can provide more information or context, I will try my best to answer your questions.
In most cases, the Overlord anime doesn't go beyond the manga. It relies on the manga as its source and keeps in step with it. There might be minor variations, but not to the extent of being ahead.
Overlord is about a powerful gamer trapped in a virtual game world as his overpowered skeletal character. He builds a dominion and faces various challenges and enemies.
In general, the Overlord manga does have more story content than the anime. However, the anime's adaptation is well-done and has its own charm. Some people prefer one over the other depending on their preferences.
The Overlord game was related to anime. Overlord was a light novel written by 486, which had also been adapted into an animation and game. In the game, the word 'overlord' referred to a powerful existence with power and ability that surpassed that of humans. The anime told the story of the conflict between humans and dragons, and also added superpowers, magic, and other elements.
There was no love story in Overlord anime. Although Overlord was a work with racial and fantasy elements as its theme, it did not involve love plots. The main character, Amber, was just a powerful warrior whose life revolved around battles and adventures. Although some characters had bonds and emotional exchanges, these feelings only existed to express their friendship and loyalty, and did not develop into a romantic relationship.
The 'Overlord' anime novel is mainly about a powerful wizard who gets trapped in a virtual reality game world. He finds himself in a strange new situation where he has to navigate through various challenges and encounters with different races and characters in this game - turned - real - like world.