Lund came to Copenhagen to train as an artist, and in 1797, at the age of 22, he started his studies at the Royal Danish Academy of Art (Det Kongelige Danske Kunstakademi) with the support of Johan Frederik Clemens, acclaimed royal engraver and influential member of the Academy.
He studied under neoclassicist Nikolaj Abraham Abildgaard at the Academy from 1797 to 1799, and taught drawing privately during his student years.
He was part of the expatriate colony of Danish and German artists and scientists in Italy, which included Friederike Brun, Charlotte Humboldt, Georg Zoëga and Bertel Thorvaldsen.
Cultured, talented and sociable, he secured himself many important contacts during this time, including those within the Danish royal house.
A companion piece painted between 1807 and 1811, "Pyrrhus og Andromache ved Hectors Grav" ("Pyrrhus and Andromache at Hector's Grave"), was contributed to the Danish Royal Painting Collection, now the Danish National Gallery (Statens Museum for Kunst), by Baron Schubart, General Consul in Livorno.
These paintings helped establish himself as an idealistic and romantic painter, in contrast to rival neoclassicist Christoffer Wilhelm Eckersberg's realistic approach to the visual arts.
In 1809 Lund began attempts to secure the Academy professorship vacated by his former teacher Abildgaard upon his death in 1806.
In 1818 with support from Prince Christian Frederik, he was finally named professor at the Academy along with Christoffer Wilhelm Eckersberg.
He is also well known for his altarpieces and paintings of religious themes, which were influenced by his admiration for such Renaissance painters as Fra Angelico, Perugino and Raphael.
He designed the main curtain of the Royal Theatre (Det kongelige teater) with a view of the Acropolis in 1828, which still hangs to this day.
Early Italian art, his contact with the Nazarenes, fellow countryman and expatriate Bertel Thorvaldsen, and for romanticism's ideals, all left an indelible influence on his artistic production.
The Royal Library houses a collection of his letters, inclusive correspondence with younger artists that bears witness to his influence on them.
He left a lasting impression by his many monumental paintings still widely on display, and by the effect he had on a generation of artists due to his long professorship at the Academy.