One idea could be a story where Fred and George play a prank that accidentally involves Harry, Remus, Lucius and Severus. Maybe they create a magical item that goes awry and causes chaos among all of them. For example, it could make them switch personalities temporarily, leading to some very interesting and comical situations.
You could start with a scene at Hogwarts, like in the Great Hall. Fred and George are causing a bit of a ruckus, Harry is trying to stay out of trouble, and Remus is just watching with amusement. Then, Lucius arrives with some sort of business at the school, and Severus is there to greet him. This sets up the different personalities and the potential for conflict or cooperation right away.
George in the George and the dragon story is a knight. He is a brave and heroic figure who is willing to face the dangerous dragon to protect the village.
His mother is a likely sender. She could be worried about Remus and send a Howler to remind him to take his Wolfsbane Potion regularly or to be more cautious around others. Mothers are often protective, and in the wizarding world, a Howler is a rather forceful way to get your point across.
I'm not sure who George McKenna specifically is in 'the george mckenna story' without more context. It could be about an individual with unique experiences, achievements or a particular journey.
In non - lemon fanfiction, their relationship is often complex. There is usually a lot of mutual distrust at first, given Severus' association with the Slytherins and Remus being a Gryffindor. But as the story progresses, they might find common ground in their intelligence and love for magic. For example, they could bond over a difficult magical theory or a rare potion ingredient.