After completing his studies with Bernardo Valentim Moreira de Sá, Luiz Costa left for Germany, where he studied with Vianna da Motta, Stavenhagen, Ansorge and Busoni. In parallel with his career as a soloist pianist, he worked with remarkable artists such as the cellists Casals, Hekking, Suggia and violinists Enesco and Aránye as well as the Rosé and Chaumont quartets.

He taught at the Oporto Music Conservatory of which he was also director. He was a teacher of rare distinction due to both his natural gifts and his vast culture as well as deep musical knowledge. He taught and influenced whole generations of pianists as far as both aesthetics and professional ethics were concerned.

As Artistic Director of the "Orpheon Portuense" Luiz Costa had a noteworthy action. At his invitation, some of the most remarkable artists of his time visited and performed in Oporto. Namely, he was responsible for Maurice Ravel’s visit, in 1928.

In nature he always found an endless source of inspiration that can be found in the titles and atmospheres of many of his piano compositions. His friendship with his master Moreira de Sá, a celebrated encyclopaedist and a violinist keen on chamber music, left him a taste for ensemble music which later translated into his professional life as a pianist and composer. His chamber music works are proof of the above.

Costa was a cultivated musician interested in all arts and a friend of sculptors, painters, poets and writers. He was captivated by the magic of poetry. Thus were born works for piano and singing that were not irrelevant in the context of his work. His musical dialect is smooth and without any too sharp turns. The intimate lyricism and serene poetry that flows from his compositions are not immune to dash, splendour and drama on many occasions.