There could be a friend who is initially shocked. Like Malia, who doesn't quite understand the whole concept of pregnancy and family yet. She might say some inappropriate things at first, but then slowly come around and become really fond of the idea of having a baby in the group, and start to look out for Lydia in her own unique way.
Some friends might be overjoyed. For instance, Stiles could be really excited and start making all kinds of plans for the baby shower. He might also be a bit overprotective, constantly checking in on Lydia and making sure she's taking care of herself.
Some of her friends might be overjoyed and immediately start planning baby showers and buying cute baby gifts.
Ross would probably be really shocked and a bit jealous at first. He might have a hard time accepting it. Phoebe would be super excited and would probably offer to be like a spiritual guide for the baby. Chandler would make a lot of jokes about it, but deep down he'd be happy for them. Monica would be practical and start planning things like baby showers and making sure Rachel has all the right things for the pregnancy.
Well, Serena would probably be over the moon. She's always been close to both Dan and Blair and would see this as a wonderful union. She'd be there for Blair during the pregnancy, helping her with shopping for baby clothes and giving her advice. Nate, on the other hand, would be more practical. He'd offer to help Dan with any financial or housing arrangements they need to make for the baby. And then there are the more catty friends, like Penelope and Hazel, who might be jealous and make snide remarks about how Dan and Blair got pregnant so quickly, but deep down they're just envious of their relationship.
Their friends might be initially shocked. Some of their more cautious friends could be worried about the implications of a child born to such powerful individuals. However, their closest friends would likely be very supportive and offer help in any way they can, like providing a safe place to stay or resources for the upcoming baby.
One idea could be that they face challenges from their families who are initially not supportive of their relationship now that Lydia is pregnant. Another could be that they discover some sort of supernatural complication related to the pregnancy. For example, the baby might have special powers that start to manifest during the pregnancy and they have to figure out how to deal with it.
One idea could be that they face unexpected challenges during the pregnancy. For example, Derek discovers a family curse that might affect the baby, and they have to find a way to break it. Another could be that Lydia has premonitions about the future of their child, which leads them on a journey to protect the unborn baby from a hidden danger.
Lydia would probably be very scared at first. After all, being kidnapped by a strange and unpredictable character like Beetlejuice is no joke.
There could be fanfictions that focus on their teamwork. In some stories, they are paired up on a special mission within the supernatural world of their universe. They have to rely on each other's unique abilities, like Derek's werewolf strength and Lydia's banshee powers, which makes for an exciting read.
Another place could be FanFiction.net. Although the interface might not be as modern as AO3, it still has a good number of Derek and Lydia fanfictions. You may need to do a bit more sifting through different categories to find the ones you like, but it's definitely worth a try.
Derek could be initially hesitant. He has his own past traumas and might worry about how he could be a part of the child's life. However, as he sees Stiles struggling to handle it all alone, his feelings for Stiles would push him to become more involved. He would start to see the son as a new beginning, a chance to build a family in a way he never thought possible before. He'd offer his werewolf skills to keep the child safe and teach him about the supernatural world if needed.