Kammala wannan magana: Bayan kammala karatunsa daga ƙarami, an yi musayar Lukowich daga tsibirin zuwa Dallas Stars don zagaye na uku a cikin
1997 NHL Entry Draft a ranar 1 ga Yuni, 1996. Ya buga wasa a cikin tsarin Taurari tare da Michigan K-Wings na International Hockey League (IHL) a farkon wasanninsa uku na ƙwararru, yana samun kiran NHL tare da Taurari a 1997<unk>98 da 1998<unk>99. Lukowich ya halarci gasar cin kofin Stanley ta Stars ta 1999, ya bayyana a wasanni takwas a lokacin wasan, amma bai cancanci a kara sunansa a gasar ba. A cikin 1999<unk>2000, ya kasance tare da Taurari na cikakken lokaci kuma ya yi rikodin maki huɗu sama da wasanni 60 a kakar wasan NHL, yana da kusan minti 12 na lokacin kankara.