Artur and his older brother Theodor (1876-1962) were the first professional pianists in Estonia to give concerts abroad.
[1] Lemba was a finalist in the prestigious Anton Rubinstein Competition and later a professor at the Saint Petersburg Conservatory.
His composition teacher was Nicolai Soloviev and he studied music theory with Anatoly Lyadov, Alexander Glazunov and Nikolai Rimsky-Korsakov.
Notable students included Elsa Avesson, Olav Roots, Villem Reimann, Veera Lensin, Kirill Raudsepp and others.
In addition to the concerts in Estonia, Lemba performed in Saint Petersburg, Riga, Moscow, Odessa, Budapest, Helsinki and Stockholm.