After the death of his mother in 1884, he was sent to receive education in the city of Wesenberg, then part of the Russian Empire, where his aunt Adela Fyodorovna Assur guided his early years of homeschooling.

From 1892 to 1896, Leonid lived with distant relatives in Warsaw, where he completed the fourth, fifth, and sixth grades of school with honors.

In the autumn of 1895, his father enrolled Leonid in the seventh grade of the Grodno School, from which he graduated in 1897, also being awarded the medal of merit.

After completing his studies in 1901 with the degree of Kandidat (not to be confused with the modern Kandidat degree, which was awarded to individuals who completed their undergraduate studies with academic excellence), he followed the path recommended by the prominent engineer Nikolái Zhukovski and applied for admission to the Moscow Technical Institute.

In April 1906, Leonid Vladimirovich married Elena Mikhaylovna Mindlinaya, who outlived her husband by 40 years.

In 1906, Leonid Vladimirovich, along with his family, moved to St. Petersburg, where he obtained a position as an engineer in the workshops of the municipal bridge service.

In the summer of 1910, Assur undertook a study commission abroad, where he had the opportunity to assess the state of teaching Applied Mechanics in technical higher education institutions in Germany.

In 1915, Assur was appointed as the Director of Theoretical and Applied Mechanics exercises at the Polytechnic Institute of St. Petersburg.

On February 13, 1916, in front of the Scientific Council of the Polytechnic Institute, Assur publicly defended his doctoral thesis titled "Study of planar lever mechanisms from the perspective of their structure and classification" («Исследование плоских стержневых механизмов с низшими парами с точки зрения их структуры и классификации») to qualify for the scientific degree of Adjunct (equivalent to the modern Ph.D. degree).

In 1918, Assur was elected Professor emeritus in the Department of Applied Mechanics and Basic Mathematics at the Forestry Institute.

Assur was sent to Voronezh to assess the state of teaching Applied Mechanics and Mathematics in the agricultural institutes of the region.

He also developed the method of constructing planar mechanisms of any complexity using the superposition of kinematic chains with zero mobility, which were named "Assur groups."

He proposed subdividing mechanisms into families, classes, types, orders, etc., providing a comprehensive categorization system.

"Две теоремы механики твёрдого тела в применении к изучению движения плоских механизмов."