As more and more features get added to Android, it can be increasingly more involved in configuring it. With something like text messaging notifications in the lock screen, setting that back up again might involve digging pretty deep in to your Settings menu. You need to check the Notifications menu, Lock Screen menu, and perhaps the Settings menu in your chosen text messaging app. And keep in mind it might not be a 'top-level' option in any of those menus. They're also becoming more and more densely packed with more options so there could be a secondary menu in the form of a gear icon, or three vertical dot icon,or three horizontal line icon in the upper or the lower menubar, along with some contextual menus that might not be revealed until you do something like a long-press on an option.
Try opening up your Settings menu and in the upper search bar type in 'lock' or 'notification'. Both are pretty generic so there should be a lot results to scroll through that might be relevant. And don't make assumptions about what you think is directly related, there could be an incidental issue (i.e. the more personal items you opt to reveal in a lock screen, this adds in an unnecessary weak point to your privacy settings.)
