Her announcemernt comes a day after Wen Jiabao, the Chinese premier, said in an opening address to the National People's Congress that Beijing was committed to unifying Taiwan with China.
That followed a speech at the weekend by Chen Shui-bian, the current Taiwan president, in which he said Taiwan should pursue independence and change its official name from "Republic of China" to Taiwan.
Those comments were denounced by China, which said anyone who sought to permanntly split the two would "become a criminal in history".
Taiwan has been ruled separately from China since 1949 when the communists won the Chinese civil war, forcing the nationalists to retreat to the island.
Since then Beijing has labelled Taiwan a "renegade province" that will eventually be reunified with the mainland, by force if neccessary.
"There should be no hatred between Taiwan and China"
Lu, 62, has often been criticised by China's state-run media for her pro-independence stance, labelling her as "insane" and the "scum of the nation".
But she has shrugged off the attacks, calling instead for peaceful co-operation and co-existence between Taipei and Beijing to promote what she calls "constructive engagement".
Announcing her bid to become the presidential candidate for her Democratic Prorgressive Party, she said it was time for "the historical feud" between China's nationalists and communists to come to an end.
"There should be no hatred between Taiwan and China. There should be no war," she said, adding she wanted to seek a bigger global role for Taiwan on the world stage.
"I need a higher position and we need more time to reach the ultimate goal of normalisation of our country and the globalisation of Taiwan," she said.
"Let us work together to end Taiwan's pathetic past and create prestige and happiness for the people."
Analysts say however that Lu's chances of winning next year's elections are slim, and many doubt she has enough support to win even her party's primary.