Read this... especially on Chapter 8.1, 8.2, 8.3
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If FDH resigns, you need to pay LSP if it is because of Health issue, or over 65 years old, or died. (Chap 8.1 and 8.2 conditions are clear).
Also, it protects the employers against Gross Misconduct, because LSP is only payable for dismissal "other than gross misconduct" or Reduncy (but you still have to pay Severance Payment for redundancy, but not misconduct).
So, if she plays punk, you need to follow the procedure (also listed in the document) to give warning letters (preferably with witnesses) with ample times and period, then fire her.
So, I am surprised that Peggie Wong allows her FDH to "advance" on her LSP !
She could resigned later, and there is no need to pay, unless she is already 65 !