An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specific price on or before a certain date...
when you buy an option, you have a right but not an obligation to do something. You can always let the expiration date go by...
Ms. Li's option expired on October 2nd. She didn't do anything with it. She didn't go to contract.
If an option is not exercised (in writing) by the expiry date then it lapses. That is how options work. If the option had been exercised before the end date RMHB was bound to announce it as a significant development. There is no point clutching on to it Linus-like any more - it is history. This mysterious Lily Li could conceivably come up with a new option or arrangement but it is unlikely as she would have been aware of all the relevant information but chose not to proceed.
Some have questioned how genuine the whole business was as Jerry has form with LOIs that went nowhere. Incidentally there is no such thing as a "binding" option, that only exists in Jerry's fevered imagination. The mind boggles at what a non-binding option might be - an "optional" option perhaps?