She is now planning to appeal because a 12-year-old boy won a £120,000 (NZ$240,000) payout in similar circumstances.
"When we got the [refusal] letter, my mum was so angry. I was angry too, but my immediate reaction was just to laugh," said Lucy, who lives in Bedford.
"If someone has an incurable neurological disease caused by a vaccine they've been recommended to have by the government, you need to compensate them for that.
"You shouldn't have to prove you're damaged enough."
She said the past two years had been difficult. "I used to be a complete bookworm, but I can't really read any more because I have to exert so much energy," she said.
Lucy, who hopes to study radio production at Westminster University, rarely goes out and has to stop taking her medication if she wants to drink.
She told the Guardian she also has cataplexy, which makes her "slur and stagger and look like you're drunk".
Lucy is among six million Britons given Pandemrix during the swine flu pandemic of 2009 and 2010; 80 have had sleeping disorder claims refused by the Department for Work and Pensions.
A Government spokesman said: "Decisions on claims take into account the individual circumstances of each case and the latest available medical evidence."
A spokesman for Pandemrix's makers, GlaxoSmithKline, said: "We are actively researching the observed association between Pandemrix and narcolepsy. We take the safety of patients very seriously."
Narcolepsy occurs when brain neurons that regulate the sleep-wake cycle are destroyed.
Narcolepsy: a rare disorder
Narcolepsy, which occurs in one in every 2,000 people, is a sleep disorder that causes a person to suddenly fall asleep at inappropriate times.
It is a long-term neurological condition that disrupts normal sleeping patterns.
Symptoms include, sleep attacks, daytime sleepiness, nightmares, hallucinations and cataplexy - temporary muscle weakness in response to emotion.
It is often caused by an autoimmune response - this is when antibodies are released by the body but instead of destroying disease, they attack healthy cells.
In the case of narcolepsy, antibodies attack the areas of the brain that produce a sleep-regulating chemical.
There is currently no cure but the condition can sometimes be managed, for example, by taking regular naps, eating healthily and exercising.
In some cases, medications such as antidepressants or stimulants can also help.
- Daily Mail