yeah lol^^^
I personally think he's mistaking a yearning to carry on his bloodline with wanting immortality, to live on forever..thats why he doesnt understand why Liz is intruding into his thoughts at a time where his life is in danger IMO
But if you just think that Jack probably wants to ensure his bloodline before he dies..then it makes sense as to why Liz is popping into his mind when he feels his time is running out..