Lila began his career with local side Besa Kavajë, where he made his debut in 2002 as a 16 year old and soon became a regular first team player, which earned him a move to Greek club Iraklis in January 2007. He soon returned to Besa Kavajë after failing to settle at Iraklis, and he shortly became the club captain, guiding them to a third-place finish in the Albanian Superliga before moving to KF Tirana after just one year back in Kavajë. He was a fan favourite at KF Tirana as during his three years at the club, and he won the Albanian Superliga title in his first season there, as well as helping his side reach the Albanian Cup final which he missed and his side lost in. His last game with the club came in the 2011 Albanian Cup final which his side lost on penalties after extra time, before moving to Greece for a second stint, this time with PAS Giannina.
He quickly established himself in the first team at PAS Giannina and helped his side achieve a mid table finish in his first season back in Greece, and then reach the Superleague playoffs in his second season at the club before a bottom half finish in his third season. He joined struggling Serie A side Parma on loan for the second half of the 2014–15 campaign, but he could not help the club escape relegation and returned to his parent club PAS Giannina following the bankruptcy of Parma. Since his return he has struggled to recapture his place in the first team, and has been limited to mostly substitute appearances in the league.
Lila has represented Albania at under-17, under-19, under-21 and senior levels. He made his senior international debut in 2007 against Romania and has since earned 59 caps but has yet to score a senior international goal. He became Albania's first choice right back in 2010 under Josip Kuže, and he also began to play in the defensive midfield position. Under Gianni De Biasi he has primarily played as a right midfielder or right winger since 2014, and he has helped Albania qualify for its first major international tournament as they reached Euro 2016. He was also heavily involved in the infamous Serbia v Albania match on 14 October 2014, which resulted in the match being abandoned and Albania eventually being awarded a walkover victory over Serbia.
Lila started his career with hometown club, Besa Kavajë. He made his debut for the club during the 2002–03 season in the Albanian Superliga on 14 December 2002 in an away match against Teuta Durrës. Lila came on as a substitute at half time by replacing Ervin Bardhi. However it was not a game to remember for the young Lila as it finished 5–0 to Teuta Durrës.
Since making his debut in 2002 he started to impress more and more people with his performances as a right back, this paved the way for his move to Greek club Iraklis FC in January 2007, where he joined fellow Albanians Enea Koliqi, Elvis Kaja and Indrit Fortuzi who were already at the club. Despite making his dream move abroad a reality, Lila struggled to settle in Greece and after only 6 months and 3 appearances he moved back to his original club Besa Kavajë.
Following his return, he was made captain of the team. During the 2007–08 season he played 26 times without scoring a goal. He was also a beaten Albanian Supercup finalist after losing 4–2 to Tirana. The defender played his final game with Besa Kavajë in the Intertoto Cup on 12 July 2008. He came off in the 57th minute of the game. The game ended in a 3–0 home loss and ended the club's run in Europe and Lila's time in Kavajë.
Lila completed his move to Tirana on 21 July 2008 after him and his agent Sokol Haxhia agreed to terms with KF Tirana and its president Refik Halili. Since making his move to the capital, Lila has been able to settle quickly and he has played the best football of his career so far. His first game as a Tirana player was the opening game of the season against Vllaznia Shkodër, he played the full 90 minutes of the goalless draw. His first goal in a blue and white jersey came on only his third game with the club in a Tirana derby against Partizani Tirana, he scored the winner in the 90th minute and secured the three points for his club.
Lila didn't have to wait long for another goal as it came less than a week later on 20 September 2008 against Apolonia Fier, his goal came in the 28th minute of the game. During the entire 2008–09 season he became the club's first choice right back and he played 29 games, he also proved that he has attacking qualities as well by scoring 4 goals during the campaign. Tirana concluded the league season by winning its 24 title in history, leaving Vllaznia Shkodër four points behind. Tirana also went into the final of 2008–09 Albanian Cup, where "The White and Blues" were defeated 2–1 by Flamurtari Vlorë, in a match where Lila was an unused substitute.
Lila started his second season with Tirana on 15 July 2009 by making his European debut with Tirana against Stabæk in the first leg of 2009–10 UEFA Champions League's first round. He was a starter even in the returning leg with Tirana who was defeated 4–0 at Telenor Arena, resulting in a 5–1 aggregate exit. Later, on 16 August, Lila won his second trophy with Tirana, the Albanian Supercup, where he aided the team to beat Flamurtari Vlorë 1–0 at Qemal Stafa Stadium.
He signed a three-year contract with Greek side PAS Giannina on 24 June 2011 worth €700,000 plus bonuses. He played his first game for the club on 27 August 2011 against Aris Thessaloniki in a goalless draw.
On 25 January 2013 Lila scored against Fostiras in the 2012–13 Greek Football Cup to help his side to win 3–2 to qualify in the next round.
On 12 July 2014, Lila had even declared that his contract with PAS Giannina had come to an end, allowing him to sign a contract with Croatian side HNK Rijeka, however he eventually opted against this and signed a new three-year contract with PAS Giannina.
After much speculation over his future, on 28 December 2014 he confirmed his move to Serie A club Parma F.C. He joined the club on 1 January 2015, when the transfer window reopened. He said that moving in Serie A is a dream come true, adding that Serie A is the best league in the world. On 12 January 2015 Parma announced that the deal was a temporary deal with an option to purchase, due to ongoing financial difficulties of the club.
He made his debut for Parma on 14 January 2015, starting in the Coppa Italia match against Cagliari. After 13 minutes however Lila was forced off the field with a thigh muscle problem. In his first game back after returning from injury, Lila scored his first goal for Parma against Sassuolo on 15 March 2015, having played from the start, with the match ending as a 4–1 defeat for the Gialloblù.
In the first days of August 2015, Lila started training with Skënderbeu Korçë, although he eventually didn't signed a contract with them. Following that, Lila left the team to return to PAS Giannina for the new season, where he was acollated his old squad number 3.In the summer of 2017 he signed a new 3 year contract.
Lila was first called up to the Albania national team by Otto Baric in late 2007; it was his performances as a right back for Besa Kavajë in the Albanian Superliga that caught the eye of the Croatian. He made his debut for the senior team in a Euro 2008 qualifiers against Romania in Bucarest on 21 November 2007. Lila started the game at right back and played the full 90 minutes. However it wasn't a debut to remember because the match ended 6–1 to Romania and the coach that had called the young defender up to the senior squad quit as the head coach of the Albanian National Team just one hour after the final whistle of the embarrassing defeat.
The next manager of the national team also liked Lila's play and this earned him a call up by Arie Haan to his first game in charge which was a friendly against Poland on 27 May 2008. Lila started the game but was substituted at half time for Endrit Vrapi. The game ended in a 1–0 loss but the Albanians played well after conceding in the 3rd minute. Andi Lila managed to play another two games under Arie Haan, in a friendly against Liechtenstein and a 2010 World Cup qualifier against Malta. In both matches he came on as a substitute.
On 21 May 2016, Lila was named in Albania's preliminary 27-man squad for UEFA Euro 2016, and in Albania's final 23-man UEFA Euro 2016 squad on 31 May.
Lila was an unused substitute against Switzerland in the opening match then played as a starter against hosts of France where they lost 2–0 and played the full 90-minutes match against Romania in an Albania's historical 1–0 win with a goal scored by Armando Sadiku. Albania finished the group in the third position with three points and with a goal difference –2, and was ranked last in the third-placed teams, which eventually eliminated them.
He is married with his partner Ornela Lila, and they become parents for the first time on 20 March 2015 when Lila's wife gave birth to the couple's first son, named Ayan. On 16 July 2015 Lila was decorated with the "Honorary Citizen of Kavaja" award for protecting the national symbols and for his contribution to Albanian football.As of 19 September 2017
As of 5 September 2017
Albanian Superliga: 2008–09
Albanian Cup: 2010–11; Runner-up: 2008–09
Honorary citizen of Kavajë: 2015