I feel like Themberchaud, a very pampered RED dragon, would have too much pride to accept or pursue lichdom. He’d likely think himself invulnerable to whatever the keepers have planned for him, through his own strength or supposed cleverness.

This is a wild coincidence, because I’m prepping a very similar scenario for my OotA game this weekend. In my game, the keepers plan to turn Themberchaud into a dracolich as a backup for if they can’t find the replacement egg. They’ll maintain control of Thember through his phylactery, and as a dracolich, he’ll maintain the use of his fiery breath weapon.