Lumsden, who benefits from the LTA Top 25 programme, rallied from a set down to beat former top-30 played Radwanska 4-6 6-2 and reach the main draw of the ITF Women’s World Tennis Tour event in West Yorkshire.
Victory over the 12th seed in the qualifying draw backed up a win over sixth seed Gabriela Ce in the first round of qualifying on Sunday.
“The first set, I started off quite well and then played some not so great few games at the end of the set to lose that one,” said the Scot, 24. “But then I came back better in the second set to win that one, and in the tiebreak I played some good points at the crucial moments to get through it.”
The run through qualifying marks another significant step for Lumsden, who only returned to the tour a few months ago following a lengthy battle with long covid.
Elsewhere, British youngster Jack Draper scored the biggest win of his career by beating world No 14 Taylor Fritz at Queen's Club. The 20-year-old surged past the American 6-3 6-2 to reach the second round of the cinch Championships.
Draper, now one of four British men inside the world's top 100, said: “It was amazing, I enjoyed my time out here. (I'm) at the start of my career, haven't played in front of this many people that often. I'm just glad of the way I played."
There was disappointment for British No1 Cameron Norrie, last year's runner-up, who bowed out in three sets to Grigor Dimitrov.
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