The 35-year-old produced jumps of 120.5 and 129.5 metres to finish behind Austria's Stefan Kraft and Norway's Halvor Egner Granerud.
The second-highest placed Pole, Dawid Kubacki, was 13th.
Two more ski-jumping World Cup events are scheduled to take place in Lahti this weekend, a team event on Saturday and an individual competition on Sunday.
Next week the world's top ski jumpers will head to Norway for the annual Raw Air tournament.
The 2021/2022 ski-jumping World Cup features a total of 35 competitions, including seven team events, in various countries.
The schedule includes the Ski Flying World Championships in Vikersund, Norway in mid-March, and the season-ending Ski Flying World Cup Finals in Planica, Slovenia.
Polish ski jumpers finished runners-up last World Cup season as a team.
Meanwhile, Poland's top ski jumper Kamil Stoch, a three-time Olympic champion, finished third in the overall World Cup standings on an individual basis.
Norway’s Granerud won the Crystal Globe as champion of the 2020/2021 season.