Among his few compositions always mentioned by his contemporaries are his both symphonies, violin concertos, piano pieces and an oratorio,[1] although none of them is known to be preserved.
As a twelve-year-old child he could perform "even the most difficult concertos and solos, not without admiration from those who listened to him", which was read in the Adresseavisen after the boy had had his debut as soloist and member of Det musikalske Selskab at a concert in Rådhusstræde (City Hall Street) on 1 February 1770.
On 11 February 1784 he gave a concert at the Royal Danish Theatre, where he received tumultuous applause for his extraordinary skill, his tasteful performance, particularly in the adagio, and his uncommonly elegant bowing.
In 1785 he began teaching violin playing in the Chapel, succeeding Hartmann in 1793 as concert master, an honor which at the time was very rare.
Lem's importance for the development of live concerts in Copenhagen was very significant and groundbreaking in several directions, not only as a virtuoso and soloist, but also as a chamber music player and leader of Det harmoniske Selskab.