To connect the apps on a deeper level, you need to have the online backup subscription on both apps.
When you have this you need to make sure you're signed in to both of them, with the same mail. You can confirm this by doing the following:
Go into Sleep Cycle and Settings, and click on Premium. If you're signed in, you will find your e-mail there. If you're not, you sign in by going to Settings and click on Online backup.
And then, go into Life Cycle and Settings and click on Account. You'll see your login e-mail there. This one should be the same as in Sleep Cycle.
If you are, then also make sure that Life Cycle specifically is connected to Apple Health. Go into Life Cycle and Settings, and Advanced. Click on Apple Health, and make sure you're syncing your sleep data from Health.
If it's still not working, then contact us and provide us with your login email address, and we will look into this.