I have not sold on LMS yet, but have read documents on their...

I have not sold on LMS yet, but have read documents on their website.

From this, my understanding is that there are 2 ways to sell on LMS:
1. If selling the entire seller's holding, they have a facility to deal with all aspects of the transaction, called Share Sale Centre. If someone were to offer to buy my entire holding, this is what we would use.
2. If selling only a portion of the seller's holdings, LMS only facilitate the transfer of shares from the seller to the buyer, and the payment/financials are dealt separately. Once the form is received by LMS, LMS will call the seller or sellers to verify the validity of the form before proceeding with the sale.

Hence, for a small parcel transfer, I'd imagine the process to be something alike:
a. Buyer and Seller fill in the form together.
b. They do the ID check at the police station or similar to get the JP signature for the ID check.
c. They use the JP to witness a settlement contract that describes e and f below.
d. Whoever is paying the $65 fee takes the largely completed form, fills in the payment details and lodges it to LMS. This is to ensure the payment details are not shared to the other party (i.e. card number, expiry and cvc - sufficient information to go internet shopping).
e. The buyer pays the seller on or before LMS contact the seller.
f. When LMS calls the seller, the seller confirms the transfer to LMS.

If the seller does not action affirmatively at step f, the contract at step c is used against the seller.
The seller's identification was positively confirmed at step a and b to ensure recourse is possible, as well as being necessary part of filling in the LMS transfer form.

Due to the call LMS will make to the seller being a part of the process, a third-party intermediary holding the form and the money is meaningless.