I think I had a similar situation where I had state (cart) that lives in the parent LV but is updated from live components (product form LC and cart LC). All cart logic lives in the cart LC and I call the module function needed (cart LC → add product to cart) while handling the form submission in the product form LC.
In the cart LC functions, I broadcast the updated cart data to the parent LV with pubsub and attach_hook which then updates the LV cart state.
Hope this makes sense, tough to explain on mobile.