After the sub-customers are generated in QuickBooks from LeanLaw, you need to make sure that the billing is set to "Bill this Client" and not "Bill the parent."
Use the edit function for the newly created sub-customer (matter) in QuickBooks and you will see the option. This actually will resolve the balance forward issue.
In LeanLaw, convert the Client from Client billing to Matter billing in the matter management page. (1st Image)
In LeanLaw, open each matter and create the sub-customer in QuickBooks (that is the matter). (2nd Image)
In the newly created sub-customer (matter) in QuickBooks, switch the billing from Bill with Parent to Bill this Client. (3rd, 4th Image Image)
Move the transactions from the Client to each sub-customer. You'll need to change which Customer the invoice is assigned to on each Invoice and Payment. (5th Image)