Loosen ties means to make cords or ties less tight. It's a physical thing. For example, with your shoestrings, you can loosen these ties if they happen to be too tight. You can also lose your shoestrings, meaning you lost them and don't know where they are anymore.
You don't talk about emotional or social ties like that. You can lose social ties though, in the sense of loss. But you don't loose social ties, it doesn't make sense. That's the difference between the two words.