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Jones, a 20 year-old from the north of England who has a rare congenital condition that means she has only three fingers on each hand and seven toes, steamed past Lu 6-0 6-1.
When she was a child, she was told she would never be able to become a professional athlete.
Jones, the British number five, was ranked 241 in the women's singles rankings before their clash, with the more experienced Lu 40 places ahead of her.
"I have big goals that I want to achieve and I do want to change people's perspectives not just on tennis but on sport and how they approach sport," she said in an interview.
"My syndrome (Ectrodactyly Ectodermal Dysplasia) is very rare... and it's a complicated one because there are many different symptoms.
"My symptoms are I have three toes on my right foot, four on my left, four fingers on both of my hands."
Jones, 20, who also saw off former top 30 player Monica Niculescu of Romania and Croatia's Jana Fett in the earlier qualifying rounds.
She now has nearly three weeks before the start of the Australian Open, the first time she has reached the main draw of a Grand Slam, which begins in Melbourne February 8.
"You get the staring, you get the questions, you get the sympathy sometimes -- and then you get the opposite, you get the hatred," Jones said.
"I've never been one to focus too much on what other people think of me or specifically of that, because I don't think this defines me."
Also booking their spots on a specially chartered plan to Melbourne -- and quarantine -- was Tsvetana Pironkova.
The 33-year-old Pironkova is playing in just the third event since returning from a three-year absence, during which she gave birth to her son Alexander.
The three tournaments she has played have been majors with the Bulgarian reaching the quarter-finals at the US Open last year and third round at Roland Garros.
On Wednesday, Pironkova defeated Magarita Gasparyan 6-3, 7-5.
Canada's Rebecca Marino, 30, will play in the main draw at a Slam for the first time since the 2013 Australian Open.
Marino defeated Maryna Zanevska 6-4, 7-6 (11/9).
In men's qualifying, being held in Doha, Spanish 17-year-old Carlos Alcaraz became the first man born in 2003 to reach the main draw of a Slam.
Alcaraz stormed past second seed Hugo Dellien 6-2, 6-3.
The controversial Bernard Tomic, a former top 20 player, made his home Slam by seeing off fellow Australian John-Patrick Smith 6-4, 5-7 7-6 (10-7).