Fourth-seeded Radwanska, the highest seed left following the exit of defending champion Williams, Victoria Azarenka and Maria Sharapova, beat Li, the sixth seed, 7-6 (7/5) 4-6 6-2 in a gripping two-hour, 43 minute contest which was completed under the Centre Court roof.
Radwanska, the runner-up in 2012, took victory on an eighth match point.
The 24-year-old Pole, who had gone into the quarter-final with a 4-6 losing record against Li, also overcame an injury scare when she needed her right thigh tightly-strapped at the start of the deciding set.
"I have played so much tennis in the last few days, that's why I have the problem."
Radwanksa and Lisicki have played twice on the WTA Tour, winning a match apiece.
"We have known each other since our junior days -- it'll be a great challenge on grass," said the slender Pole.
Li fired 58 winners in today's quarter-final but was undone by 40 unforced errors.
Lisicki followed-up her shock defeat of Williams with a 6-3, 6-3 win over Estonia's Kaia Kanepi to reach her second Wimbledon semi-final.
"It was an amazing match yesterday, but I had to make sure that I had calmed down and was ready for today," said Lisicki, who completed victory in her fourth Wimbledon quarter-final just before rain began to fall.
"I have had experience of other years to help me. I also played the semi-finals in 2011 so that helped me be ready for today.
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