When Nick enters Tom and Daisy's mansion, Daisy and Jordan are sitting on an enormous sofa, while breezes from the open French doors blow around them. Daisy doesn't make much of an effort to move:
she leaned slightly forward with a conscientious expression—then she laughed.
At this point, Daisy says she is "p-paralyzed with happiness."
This is her joking way of explaining why she isn't making any more effort to respond to Nick's arrival. What she is saying is that she is glad to see him, but not enough to get up and give him a hug or be emotive.
Saying these words are a lie is too strong a statement. Daisy is not being sincere, but she also is making no deliberate effort to deceive Nick. She knows he knows she is using hyperbole or exaggeration. She isn't that happy to see him, but she is being flattering and witty. This is what we would call social banter, and Nick will soon match her tone, exaggerating in kind.
Primarily, this utterance is meant to show from the start that Daisy has a great deal of charm. Nick knows she is exaggerating, yet at the same time, he is taken in, noting that she has a "way " of
promising that there was no one in the world she so much wanted to see.
This is similar to how Gatsby will later make Nick feel—seen, heard, and delighted in. Daisy and Gatsby share the gift of charm. However, Daisy's insincerity will begin to disturb Nick over the course of the evening and make him feel he is being played.