How are Daisy's first words "I'm p-paralyzed with happiness" a lie? What does she really mean?
On a surface level, Daisy's comment was meant to indicate that she was pleased to see her long-lost cousin, Nick, but that she didn't want to spend the energy it would take to actually get up from the couch on which she and Jordan Baker were reclining.
The other girl, Daisy, made an attempt to rise-she leaned slightly forward with a conscientious expression-then she laughed...
There could be several deeper interpretations of Daisy's words and actions. Daisy was accustomed to having people wait on her desires rather than having to exert herself too much. She may have simply felt that Nick was family and therefore it wasn't necessary to work too hard at responding to his arrival.
However, Daisy was also in a marriage that did not fill her with feelings of love and mutual enjoyment. Daisy may have felt "paralyzed" in the sense of being trapped in a relationship that did not involve affection but did give her access to lots of money and the things of wealthy society. While she enjoyed those material items and would not give them up, there was a part of her that wished for more emotional satisfaction.