This could be called a slow paced story in that regard, why? Because for those reincarnators to appear in Lambda, they need to die there, and they all have "fortunes" to lead them to live a long and happy life.
But as has been seen, Heinz did something under rules from other people, and these people can also be considered enemies, thus Vandalieu has more enemies that he still doesn't know yet, but not only that, they don't know of him either, after all, his mother was killed, an the baby likely died too, right?
Which means that there is no one actively looking for him, so for now, he had peace.
However, it's not just enemies that he finds, but also allies, many allies, a "giant family".