If you click the Delete button in LCRM for a contact record, the matching constituent record in Luminate Online is not removed. You should unmark the checkbox for "Active" on the contact record which will sync to Luminate and remove them. Once they have been removed from LO, you can click the Delete button in LCRM to have them deleted permanently. 
Note: If you remove contact records in LCRM via the API (apex data loader, excel connector, etc) the constituent record in Online is not changed. You would need to manually remove all constituent records in Luminate Online as well.