He has performed music from the Baroque (including Bach's The Art of the Fugue, BWV 1080) to the present day, specializing somewhat in music of the U.S. Lively met Elliott Carter randomly on a Paris subway and subsequently programmed his works frequently, but he was also an enthusiastic performer of works by such vernacular and vernacular-influenced composers as Gershwin, William Bolcom, and Scott Joplin. Lively's 2018 album I Got Rhythm, a survey of American piano music, was an especially strong seller in France. Another Lively specialty has been extremely difficult music, as represented by concertos of Busoni, Wilhelm Furtwängler, and Joseph Marx. He is also an enthusiastic chamber music player, especially at his own Saint-Lizier Festival in the Pyrenees mountains, which has attracted Martha Argerich and other top musicians.
Lively has taught at the Paris Conservatory and has given master classes at the Hochschule für Musik in Vienna, the Royal Scottish Academy, and Belgium's Chapelle Royale. He also is a frequent competition jurist. Lively's recordings include one of Chopin's piano concertos arranged for piano and string quintet, with the Quatuor Cambini-Paris, in 2019.