A couple of the same actors take part in both dramas. Some are even in very similar roles. Both dramas are part of the Light On series and both deal around characters that you never know if they are good or evil. Both are complex crime dramas with stellar acting and production. You will have a very similar feeling watching both.
In both dramas a child "returns" to their family. during the drama doubt arises of the identity of that child and if its truly this person. While in Homesick this is pretty much clear from the beginning, it is a mystery in "Lost in the Shadows". Both children are however involved in a murder case and try to figure out what has truly happened to the person who's identity they have taken on.