The team did not reveal terms of either contract.
The 31-year-old Lue played for Atlanta and Dallas last season, averaging 5.8 points and 1.5 assists in 50 games.
The 6-foot guard was drafted out of Nebraska with the 23rd pick in the 1998 draft. He has averaged 8.9 points, 3.3 assists and 1.8 rebounds in his 10-year career, which included championship seasons with the Los Angeles Lakers in 2000 and 2001.
Allen began last season in New Jersey before being traded to Dallas. The 6-foot-10 Allen averaged 4.6 points and 2.7 rebounds last season and has averaged 5.7 points and 3.2 rebounds in his seven-year career.