Paul Lay was born in Orthez, in the Pyrénées-Atlantiques, on July 22, 1984. His mother played him songs and arias at home, and by three he was picking out at the piano what he had heard; formal lessons started at five and left him with an ear-first approach he has never abandoned. He studied at the Conservatoire à Rayonnement Régional de Toulouse and then in the jazz and improvised music department of the Conservatoire National Supérieur de Musique et de Danse de Paris, where his teachers included François Théberge and Glenn Ferris, and he took further instruction from the Italian bassist Riccardo Del Fra. Straight out of the conservatoire he joined Del Fra's quintet, a working association that has left no commercial recording.

The competition circuit made his name before the records did. He reached the final of the Concours International de Piano Jazz Martial Solal in 2006, and in 2007 he took a special encouragement prize at the Bösendorfer Solo Piano Competition at the Montreux Jazz Festival, playing three pieces of his own ("Endless Stars," "FSP" and "My Blues") on the Bösendorfer Imperial; the festival issued the whole competition on disc, which is where his earliest surviving recorded solo work sits. The soloist prize at the Concours National de Jazz de La Défense followed in 2008, and the Moscow international jazz piano competition in 2015.

His first album, Unveiling, came out on the Limoges label Laborie in 2010, a piano trio with Simon Tailleu on bass and Elie Duris on drums. In 2012 he took over the piano chair in Ping Machine, Frédéric Maurin's large Paris ensemble, succeeding Benjamin Moussay, and he stayed for three records: Encore, Live au Petit Faucheux (2013), then Easy Listening and U-bi__K, both issued on Neuklang in 2016. His second album under his own name, Mikado (Laborie, 2014), is a quartet of entirely his own compositions with Antonin-Tri Hoang on alto saxophone and bass clarinet, Clemens van der Feen on double bass and his former teacher Dré Pallemaerts on drums. It won the Grand Prix Jazz of the Académie Charles Cros, and the Académie du Jazz named him winner of the Prix Django Reinhardt in February 2016, the year of that academy's sixtieth edition. Jazz Magazine's critics had already voted him French revelation of the year for 2015.

The same period built the Paris band that connects him to the Israeli saxophonist Shauli Einav. Lay is the pianist on Einav's A Truth About Me (Cristal Records CR218, 2013), alongside Florent Nisse on bass, Louis Moutin on drums, Andy Hunter on trombone and Antonin-Tri Hoang, and on the follow-up Beam Me Up (Berthold Records, recorded at the Studio de Meudon on June 4 and 5, 2015), where he plays piano and Fender Rhodes with Nisse and Gautier Garrigue on drums, the four of them billed as the Shauli Einav Quartet, with Pierre Durand's guitar on the closing track alone. He also became a first-call sideman in Paris: Géraldine Laurent's quartet with Yoni Zelnik and Donald Kontomanou on At Work (2015) and Cooking (2019), and Éric Le Lann's quartet on Life on Mars (2015), with Sylvain Romano and Kontomanou.

February 2017 brought two albums on the same day, both on Laborie. Alcazar Memories is a drummerless trio with the Swedish singer Isabel Sörling and Simon Tailleu, named after the Marseille music hall and built out of Provençal songs of the 1920s and 1930s ("Adieu Venise Provençale," "Le Petit Cabanon") alongside new pieces sung in English and Swedish; Lay wrote the music for seven of its eleven tracks and Sörling most of the words. The Party, with van der Feen and Pallemaerts, takes its title from the Blake Edwards film and is entirely his own writing, ten pieces conceived as small cinematic scenes plus one standard. The pair drew a Coup de Cœur Jazz et Blues from the Académie Charles Cros and more than seventy concerts. That summer he was one of the musicians aboard the Queen Mary 2 for The Bridge, the transatlantic crossing marking the centenary of American entry into the First World War, for which he wrote an anthem and played nightly.

Thanks a Million, cut at the Studio de Meudon in March 2018 under Laurent de Wilde's artistic direction and released on Gazebo, is a trumpet-and-piano duo with Éric Le Lann in tribute to Louis Armstrong. Later that year Label Bleu issued Espaces, a collectively billed trio with the drummer Edward Perraud and the bassist Bruno Chevillon recorded at Studio Sextan in January 2018, and in 2019 he took the piano chair of the Moutin Factory Quintet for Mythical River (Laborie), succeeding Thomas Enhco and Jean-Michel Pilc in a band otherwise made up of François and Louis Moutin, Christophe Monniot and Manu Codjia. Deep Rivers (Laborie, January 2020) turned to American song from the Civil War era to Nina Simone, with Sörling, Tailleu, Kontomanou and a three-piece horn section. In 2020 the Victoires du Jazz named him instrumental artist of the year.

The catalogue since then has widened rather than settled. Full solo (Gazebo, 2021) is an unaccompanied recital built on Beethoven, with "Hymne à la Joie," the Moonlight Sonata, the Seventh Symphony, "Lettre à Élise" and a Bagatelle rethought at the keyboard. Blue in Green, taped at La Scala in Paris on February 23, 2022 with van der Feen and Pallemaerts, is a Bill Evans tribute. L'Odyssée, recorded in October 2020 with the Hungarian bassist Mátyás Szandai and Kontomanou and finally issued by Gazebo in October 2024, a year after Szandai's death, sets Homer's poem as a suite of his own pieces. In September 2022 he was appointed professor of jazz piano at the Conservatoire National Supérieur de Musique et de Danse de Paris, the school he had graduated from. Recent commissions have pushed him toward larger forces: Waves of light, for jazz trio and the chamber choir Les Éléments under Joël Suhubiette, recorded at the Théâtre de la Cité in Toulouse in February 2025 and released in January 2026; a "Rhapsody in Blue extended" for trio and orchestra premiered at Jazzdor with the Orchestre Philharmonique de Strasbourg; and Un Français à New York for the Orchestre National des Pays de la Loire. He has also written the score for Mark Gill's film Ravens, and in 2024 recorded a two-piano concert with Jean-François Zygel released by Le Triton as Pianos Croisés.

Lay's own list of models runs from the earliest piano jazz to the avant-garde without a break: Jelly Roll Morton and Earl Hines, Thelonious Monk and Duke Ellington, Cecil Taylor, Paul Bley and Ran Blake, with a parallel debt to singers, Billie Holiday and Bessie Smith through Ella Fitzgerald and Sarah Vaughan to Cécile McLorin Salvant, Leïla Martial and Isabel Sörling, and a third strand from the classical repertoire, Bach and Mozart, Ravel, Scriabin and Stravinsky, Ligeti, John Adams and Morton Feldman, and back as far as Machaut and Josquin. Philippe Méziat, writing in Citizen Jazz, described the playing as very coloured and very melodic, drawing on groove for its deep voicings and on song for an agile right hand, while other French critics have pointed to a certain classicism in it. Martial Solal, whose competition Lay reached the final of in 2006, credited him with harmonic imagination, varied playing and an evident knowledge of jazz history alongside a voice of his own. Reviewing Mythical River for All About Jazz in 2019, Dan Bilawsky singled out "Echoing" as the track that highlights his contribution to the Moutin brothers' band. The through-line across records as unlike each other as a Provençal song trio, a Beethoven solo recital and a choral commission is that he writes for the specific room and the specific players in it rather than adapting a fixed manner.