Lauitiiti played for the Mangere East club in 1996 and shone as a junior in their U19 side in 1997, scoring 17 tries in 19 games. He went on to gain international honours with the Junior Kiwis that year, and again in 1998.
In 2002 he was named the NRL's second-rower of the year. He was an integral part of the Warriors squad that reached the 2002 NRL Grand Final, the first time in the club's history, however they lost the match to the Sydney Roosters. Lauitiiti, who would go on to play 14 times for New Zealand, was part of the Kiwis side that toured Great Britain in 2002, featuring in seven out of the eight games on the tour, including all three Tests against the Lions, plus games against St Helens, England A, Wales and France. He also scored in the third Test against Great Britain.
When Lauitiiti was released from his contract with the Warriors it sparked a world wide chase for his signature. However, the Leeds Rhinos beat competition from 14 other clubs in Australia and England to secure the second rower. He had appeared in 115 games for the Warriors and scored 33 tries by the time he left the club after the 2003 NRL season.
Lauitiiti joined Leeds in May 2004 on a two-and-a-half-year contract. He made his debut for Leeds against Salford and took little time to settle in, scoring his first try in the subsequent game against Bradford. His incredible ball-handling skills earned him a place in the Tetley's Super League Dream Team in 2004. He played for the Leeds Rhinos at second-row forward in their 2004 Super League Grand Final victory against the Bradford Bulls.
As Super League IX champions, the Rhinos faced 2004 NRL season premiers, the Bulldogs in the 2005 World Club Challenge. Lauitiiti played from the interchange bench in Leeds' 39-32 victory. In 2005 Ali scored 14 tries in 32 appearances including 17 as a replacement. His 14 tries includes an incredible five tries against Wakefield when he came off the bench to become the first forward in the summer era to score five tries. He also appeared in the 2005 Challenge Cup Final. He was subsequently named in 2005's Super League Dream Team. He helped Leeds to their second successive Super League Grand Final appearance when he scored the winning try against St Helens with an 80 metre run in the Grand Final Qualifier, then played in the 2005 Super League Grand Final which ended in defeat for Leeds. In the 2005 Tri Nations tournament Lauitiiti once again joined the New Zealand squad and scored a try against Great Britain after coming on from the bench, and was then part of the successful squad who defeated Australia in the historic final victory.