The German responded immediately though, reeling off four straight games and closing out the match, rather nervily, on her third match point.
"I am very happy," Lisicki told BBC Sport.
"It was an amazing match yesterday and I had to calm myself down, but I think the experience that I got from three previous quarter-finals here helped me.
"There is no pressure for me because it is a game that I love so much and I want to keep it that way."
Radwanska battles past Li
24, demonstrated why she has become a fixture in the world's top four over the last year, despite lacking the stature and power of her leading rivals.
Battling with a thigh problem and a more powerful opponent, the Pole sealed victory in a dramatic final game on her eighth match point after two hours and 43 minutes.
She had fended off four set points with some superb returning and recovered from 5-3 down in the tie-break to win the first.
Li hit back with four games in a row to take the second, at which point Radwanska had a medical timeout to get her thigh strapped, and the Pole promptly broke at the start of the decider.
A second burst of rain caused a delay as the Centre Court roof was brought across, but the momentum stayed with Radwanska on the resumption and she clinched victory in a dramatic service game.
"I'm very happy to have got through, and even when I was struggling a little bit in the third set," she told BBC Sport. "I'm very, very happy to be in the semi-finals."
Asked about her thigh injury, she added: "Too much tennis the last few days, that's why I was struggling with that, but I think it's a good problem to have.
Jana NovotnaFormer Wimbledon champion
"All the players are going to see this as an enormous opportunity to make it to the final. I know Agnieszka Radwanska reached the final last year and has more experience, but don't underestimate Sabine Lisicki. Regarding Kirsten Flipkens and Marion Bartoli, hopefully Flipkens will be able to recover from this quarter-final."
"I'm just going to keep going and try my best in the semi-finals."
28, remains on course to reach a second Wimbledon final after coming through a rain-interrupted match against American 17th seed Stephens.
The Frenchwoman moved ahead with the only break of the first set in game 10, and edged a second that saw 10 breaks as Stephens won just five points on her own serve.
"Obviously the grass is really suiting my game," said Bartoli. "It was a very tough battle."
In an unexpected semi-final line-up,
is the most surprising name after seeing off eighth seed Kvitova in her first major quarter-final.
The Belgian, who was ranked 262 in the world last year after suffering blood clots in her calf, played a terrific final set.
Kvitova was feeling unwell in the latter stages and required treatment from the doctor, but despite pushing hard the Czech could not recover the solitary break in the decider.
"It's amazing, more than a dream coming true," said Flipkens. "Semi-finals of a Grand Slam, ridiculous. Last year I didn't get into qualifying of Wimbledon."
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