"A third party can come in and could that third party be Takeda?"
What makes you think that AMLN's recent partnership agreement with Takeda does not contain the same anti-takeover provisions as its old deal with LLY? If it does, as AMLN no doubt preferred, then Takeda can not be the "third party." A true third party buyer would have to deal with both LLY and Takeda as partners, making a buyout of AMLN far less attractive. AMLN designed into its big partnership agreements formidable anti-takeover provisions. This will give shareholders with patience the full benefits of their diabetes and obesity franchises.
No third party wanted Byetta with LLY as a partner after many years, even with AMLN's stock trading at dirt cheap levels. AMLN would not enter into a partnership agreement with Takeda if it allows them to turn around and disrupt its LLY deal and force the sale of the firm.
You are right - we will see. But I'm sure that won't stop many people from repeatedy posting that AMLN will be bought out for many more years, despite the stronger anti-takeover defenses. Sometimes we don't get what we wish for!
Under current situations and judging by risk/benefit, a visionary CEO would do a merger or even hostile takeover for Amylin at a cost including anti-takeover provisions in exchange for another Lipitor if by Merck or Pfizer.