He got employed at the city writer named Reber for a modest income, and in 1743 he accepted a position as a bookkeeper for an ironworks company at Sept. That time, he observed the comet of 1744 (Klinkenberg-De Chéseaux) and attempted to calculate its orbit.
In 1745, he went to Basel, Switzerland and got a job as scientific writer for Professor Johann Rudolf Jselin, where he found more time for his private studies of math, sciences and newly, philosophy.
In 1748, Lambert accepted a position as teacher in the house of the Graf (count) Peter von Salis, in Chur, Switzerland, where he stayed for 8 years. During these years he started a number of important investigations which became the foundations of his later scientific and philosophical work, including the 1749 idea of a disc-shaped Milky Way. In 1753, he became a member of the "Helvetische Gesellschaft," in 1754 of the "physikalisch-mathematische Gesellschaft" in Basel, for which he published the results of meteorological observations in 1755; his first published paper treated the measurement of heat.
In 1756, Lambert left Chur for travelling western Europe, together with two students. Their first destination was to Göttingen, Germany where they made academic contacts: In 1757, Lambert was elected a member of the "Göttingische Sozietät" (Göttingen Society). In the following, they had a two-year stay in Utrecht, Holland, from where they visited all major places and academic people in Holland. Afterwards, Lambert and his students travelled Paris, Marseille, Nizza, Turin and Milan, before returning to Chur and the family Von Salis in late 1758.
In May 1759, Lambert left Chur again. After a short visit to Zurich, where he worked with Johannes Gessner and published his "Freye Perspektive" (Free Perspective), he went back to his home town Mühlhausen to visit his family, and stayed with his mother and the 2 sisters and 4 brothers who were still alive at that time. Shortly after, his mother died, and Lambert left Mühlhausen to go to Augsburg, Germany. There he published some of his most important works:
In 1762, because of trouble over the nomination of one of the professors, Lambert left the Bavarian Academy but stayed a correspondent. He returned to Chur where he stayed to fall 1763 an completed his philosophical work, "Neues Organon" (New Organon), then travelled via Augsburg to Leipzig, where he found a publisher for the "Neues Organon." In January 1764, he arrived in Berlin. On recommendation of his Swiss compatriots Sulzer and Euler, he was introduced to Frederick II, the King of Prussia, but it took about a year until the King became convinced of his abilities and made him a member of the Berlin Academy of Sciences in January, 1765.
At the Berlin Academy, Lambert busily continued his work in philosophy, mathematics and physical sciences, including astronomy, and published numerous papers.
In philosophy, he was a representative of rationalism, and contributed to the theory of knowledge. In mathematics, he worked on the theory of conic sections, trigonometric functions for complex variables (Demoivre's Theorem) and hyperbolic functions. In 1765 he found a proof for the irrationality of the numbers Pi and e. His discussion of Newtonian physics in the language of differential calculus ("vis viva", 1783) and his investigations on parallels, a predecessor theory of non-Euclidian geometry ("Theorie der Parallellinien", 1786), was published only posthumously. He continued his meteorological studies and in 1771, he proposed a meteorological world organisation, included the winds in his considerations, and in 1775, he published his book "Hygrometrie", a treatise of air humidity.
In 1774, he founded the "Astronomisches Jahrbuch" together with Johann Elert Bode.
In 1775, Lambert caught an illness but refused medical treatment. Despite increasing health problems, in May 1777 he finally completed his "Pyrometrie", a treatise of the theory of heat.
Johann Heinrich Lambert died on September 25, 1777 in Berlin at the age of only 49; he had never been married and had no childs. Honored during his life by the number of academic memberships, he is now remembered in the names of a number of physical laws and a unit, mostly going back to his "Photometria" of 1760:
His early observations and calculations on the comet of 1744 caught his interest on cometary orbits; he developed a geometrical method to their determination ("Eigenschaften über Kometenbahnen", 1761). In particular, he calculated orbits for the comets 1769 Messier (C/1769 P1), 1770 I Lexell (D/1770 L1) and 1773 Messier (C/1773 T1); there are records of his observations of the latter. In 1773 he noted that the changes of cometary orbits differ slightly from what is expected from gravity alone (Lambert's Theorem of Cometary Motion).
In his "Cosmologische Briefe", Lambert gives a theoretical description of the universe as it was known at his time. One important aspect is his effort to extend the Newtonian physics, which was well established for the planets, on the one hand on comets, and on the other hand to the stellar universe beyond the solar system. Moreover he gives a hierarchical theory of cosmology. A child of his time, he had a so-called "teleological" view of the universe, assuming "somebody" who defines a "purpose" of everything.
Perhaps the most important part of this work, based on his 1749 idea, is the theory of Milky Way as a disc, a system formed by thousands of stars surrounding the sun, with the Milky Way plane resembling the "ecliptic for the stars", and assuming that every star is a sun with a planetary system. Also, he assumed that there may be other Milky Way systems, potentially forming a higher-order system.
When publishing his theory of the Milky Way in 1761, Lambert was unaware of similar ideas by Thomas Wright (1750) and Immanuel Kant (1755), of which he learned only after publication. There are some differences though: E.g., Lambert was inconclusive on the nature of the "nebulae", once viewing them as extragalactic stellar systems (as Kant always did), and another time as central bodies for galactic substructures. Also in difference to Kant, Lambert argued for a finite cosmos. But like Kant and Wright, he assumed that all celestial bodies, even stars and comets, are inhabited.
In his physical works, "Photometria" and "Pyrometrie", he uses a number of astronomical applications, e.g. on brightness of the sun and the stars, as well as solar heat. Also, his theory of diffuse reflection, developed in "Photometria", is of interest in astronomy, and he introduced the important term "albedo" (Latin for Whiteness) for the fraction of diffusely reflected light by surfaces.
In his numerous papers, Lambert writes e.g. on aurorae and zodiacal light, the topology of the Moon, and of a (non-existent) Moon of Venus. The Astronomisches Jahrbuch he founded in 1774 became an important publication over decades under the direction of co-founder Johann Elert Bode.