Lin will make about $15 million this season in the last year of a deal that counts only $8 million against the salary cap. The Lakers have the cap room to absorb Lin's contract.
Lakers general manager Mitch Kupchak says the trade allows the team to acquire a solid player and two draft picks while maintaining financial flexibility.
Lin averaged 12.5 points and 4.1 assists last season, but lost his starting job because coach Kevin McHale preferred Patrick Beverley's defensive play.
Lin was born in Los Angeles and figures to be popular with the region's large Asian community. He was raised in Northern California and played four years at Harvard.
Lishchuk is from Ukraine and played for Valencia of the Spanish ACB League last season, appearing in the Euro Cup. He was drafted by Memphis in 2004 and traded to the Rockets in February 2008 before landing with the Lakers as part of a three-way trade with New Jersey in December 2010.
Also, the Lakers signed Julius Randle to a rookie contract. The forward was drafted seventh overall and is with the Lakers' Summer League team in Las Vegas.
Randle started all 40 games in his lone season at Kentucky. He averaged 15.0 points and 10.4 rebounds and was the SEC freshman of the year.