Lemke was born in Linköping, Sweden, son of golf professional Bertil Lemke, who himself competeted in seven European Tour tournaments on home soil, the 1976−1982 Scandinavian Enterprise Open, as well as met Seve Ballesteros and Jim Dent in a driving competition on Saturday evening of the tournament week at the 1977 event in Stockholm, Sweden.

As an Arizona State University alum, Lemke's 2007 stroke average of 70.03 is the third best in the school's history, behind Paul Casey (69.87, 1999–2000) and Phil Mickelson (69.95, 1991–1992).

In 2011, he had his best finish so far in a European Tour event, third at the Nordea Masters at Bro Hof Slott GC, Stockholm, Sweden, earning €93,900.

Lemke earned his European Tour card for 2019 with a sixth place finish at the 2018 Qualifying School Final Stage.

In 2019, he played 25 tournaments on the European Tour, making 15 cuts and three top-10s, finishing 118th on the Race to Dubai, with €299,187 in prize money, just missing out automatic qualifying for next season.