The subtlety of color and true originality of composition and uniqueness of his three-dimensional method of painting brought Meshberg world-wide attention.
In 1973 he, his wife and their son Andrew emigrated to the US, along with hundreds of painters and sculptors who left the Soviet Union for the United States, as a way to escape the difficulties of being an 'unofficial' artist during a time when the dominant style of social realism prevailed in Russian society.
The circles of Soviet intellectuals, professionals, and even members of the communist political hierarchy who were interested in their work reinforced the attraction of these artists to westerners.
During his lifetime he also taught art privately; his principle students were John Currin, Andrew Meshberg and Leon Lumelsky.
I knew about de Kooning and Pollock, but it seemed like after that it was all performance art and things like the ‘Spiral Jetty,’ and that completely didn’t interest me.
It was the romantic thing with Lev that appealed, the studio with oil paints and birds in cages and old books and blotted still-lifes.