He started his career in the handball club RK Inles - Ribnica. He later played in clubs Celje, Gorenje, Prule 67, US Ivry, Gold Club, Zagreb and BM Aragon. Lapajne has won 8 Slovenian Championships and 9 Slovenian Cups, 1 Croatian Championship and 1 Croatian Cup and was a runner-up at the 2004 European Men's Handball Championship.