LCH published a member note (here) regarding "invoicing back" which is component of resolving a default. There are two PDFs, of which the second sets out the order in which assets are used to fund the debts of a defaulting (direct) member, being:

1. Initial Margin of the member in each of SwapClear, RepoClear, FXClear
2. The defaulters contribution to those three default funds
3. £20m from LCH itself
4. Indemnities by non-defaulting members
5. Insurance, if any
6. Indemnities by non-defaulting members (again)
7. Any other indemnities, guarantees or "monies" available from clearing members
8. For RepoClear only: Service closure payments, or Invoicing Back
9. Any assets remaining within LCH

Invoicing Back means closing out a defaulted members positions by the CCP putting on opposite trades to reduce risk or close out the portfolio. The change is that this concept of putting on opposite trades to close out a portfolio didn't exist (as far as I can tell) as a general default management tool across many of the LCH CCP services. Quite how this is expedited I'm not sure, but it may involve the support of traders from outside LCH to execute the "opposite trades" as LCH has no trading capability of it's own.