[4] Lê Quang Liêm won a gold medal at the 2003 Asian Youth Chess Championships, held in Calicut, India, in the Under 12 category.

[6] Also in 2004, he tied with Subramanian Arun Prasad for first place in the Asian Under 16 Championship in Tehran, Iran, taking the silver medal on tiebreak score.

[7] The next year Quang Liêm won the Under 14 division of the World Youth Chess Championship in July in Belfort, France.

[16] From 20 September to 4 October at Khanty-Mansiysk, Russia, Quang Liêm with the other Vietnamese players took part in 39th World Team Chess Championship.

From May 10 to May 21, he was invited to play in the Elite group of the Capablanca Memorial tournament, a very strong field of players (FIDE category 19) including reigning champion Vassily Ivanchuk, Latin America's number one Leinier Domínguez, Czech Republic's number one David Navara, Lázaro Bruzón of Cuba and Dmitry Andreikin of Russia.

From October 12 to 21, he participated in the SPICE Cup,[17] the highest rated international invitational round-robin tournament in US history (FIDE category 18) including Maxime Vachier-Lagrave, Ding Liren, Wesley So, Georg Meier, and Csaba Balogh.

At blitz Quang Liêm finished fourth with +12=4-5, behind the new champion Magnus Carlsen, Ian Nepomniachtchi and Hikaru Nakamura.

While at Webster University, Quang Liêm played Board 1 for the national championship chess team under the leadership of Susan Polgar, winning the President's Cup all four years as a student, 2014 through 2017.

In March, Quang Liêm won the 7th HDBank tournament in Ho Chi Minh City, with total score 7 in 9 games (+5=4).

From 1 to 5 July, Quang Liêm participated in the World Open as the number 1 seed and finished at second place (behind Tigran L. Petrosian) with 7 points after 9 rounds.

[23][24] From 13 to 19 of August, Quang Liêm was invited to the Saint Louis rapid and blitz event of the Grand Chess Tour, with attendance of top super-grandmasters, including the return of Garry Kasparov.

He beat Vitaly Kunin from Germany in the first round, then Quang Liêm was eliminated by Vidit Santosh Gujrathi from India in the second.

His most successful tournament in the tour was the Chessable Masters, where he beat super grandmasters Alireza Firouzja and Levon Aronian on his way to the final where he lost to Wesley So.

In the same year, Le took the offer to be the chess coach at his alma mater Webster University, succeeding Susan Polgar.

[29] [30] In February Quang Liêm participated in the Airthings Masters round of the Champions Chess Tour 2022 where he qualified for quarter finals, which he lost to the eventual tournament winner Magnus Carlsen.

In April, at the Oslo Esports Cup, in contention for the championship, he beat Magnus Carlsen but was unable to secure a win over Jorden Van Foreest.

[31] In August (15-22), Quang Liêm participated at FTX Crypto Cup and finished fourth after Magnus Carlsen, Rameshbabu Praggnanandhaa and Alireza Firouzja, with results of +4-3.