Lipiński was born in Radzyń Podlaski. In 1810 he became the first violin and two years later the conductor of the opera orchestra at Lwów (now Lviv, Ukraine). In 1817 he went to Italy in the hope of hearing Niccolò Paganini. The two met in Milan, met daily to play, and even performed two concerts together in April 1818, which added immensely to Lipiński's reputation. Paganini dedicated his Burlesque Variations on "La Carnaval de Venise", Op. 10 for unaccompanied violin to Lipiński. Later, in 1827, Lipiński returned the honour by dedicating his "Three Caprices for Violin" to Paganini.
In 1818 on his return to Germany he stopped in Trieste to receive instruction from Dr Mazzurana, a very elderly former pupil of Giuseppe Tartini; Mazzurana was ninety years old, and could no longer play himself, but gave his criticism of Lipiński's performance of one of Tartini's sonatas. During that time, he also performed concerts together with the Polish pianist and composer Maria Agata Szymanowska.
In 1820 he travelled to Berlin where he met Louis Spohr, and to Russia. In 1829 he went to Warsaw, and played a series of concerts with Paganini that summer that were attended by the nineteen-year-old Frédéric Chopin. However, a rivalry developed between Lipiński and Paganini which destroyed their friendship. Thereafter, whenever Paganini was asked who the greatest violinist was, he would say "I don't know who the greatest is, but Lipiński is certainly the second greatest".
In 1836 he visited England and played his Military Concerto with the Royal Philharmonic Orchestra. In June 1839 he received a double appointment in Dresden, as concertmaster of the Royal Oratory and kapellmeister at the court chapel. With his Dresden duties, he ceased touring as a virtuoso, but concentrated on chamber music, with a special devotion to the string quartets of Beethoven. Here he also gave a joint recital with Liszt, performing Beethoven's Kreutzer Sonata.
He developed a great reputation as the only serious rival to Paganini. Wieniawski dedicated his Polonaise Brilliante in D to Lipiński. He retired with a pension in 1861, and died in village Virlov (Ternopil region, Ukraine).
His compositions, long forgotten but now beginning to be recorded, included four violin concertos, as well as studies, polonaises, rondos, variations, capriccios. He wrote three symphonies. His adaptation, with some of his own original music interpolated, of Ferdinand Kauer's Donauweibchen was played every season at Lwow for nearly thirty years from 1814, but the music is now lost.