Lissitzky trained in architecture in Germany and traveled in the west, but was forced to return to Russia when the war started in 1914. He did not serve in the Imperial army though he was of military age. This might have been because of tuberculosis, a disease that killed him at age 51. (Though one source mentions that the disease did not impact him until after the war, so perhaps his professional training or other factors kept him out of the army.)
The October Revolution kicked his creativity into high gear, his Jewishness no longer being a social barrier. Lissitzky's graphic designs helped anticipate the work of the Bauhaus in Germany and modernist-inspired designs elsewhere up into the 1950s when angled design elements became largely passé.
Some of his designs spilled over into painting, where his works were what was termed Non-Objective Art, a phrase used during the 1930s by New York's Museum of Modern Art for abstractions often comprised of geometrical elements. Aside from some Op-Art pieces in the 1960s and 70s, this geometrical type of decorative painting seems to have been an artistic dead-end.
This was in support of the Bolshevik armies during the post-revolution struggle against anti-Bolsheviks. The Red Army eventually succeeded against the White forces, but didn't do well in its push into Poland.
Vyeshch was an avant-garde, modern art review that seems to have been multi-lingual to a degree. Note the German and French, especially at the lower left. The title is the three large Russian letters, the third of which symbolizes the "shch" sound.
The note at the upper right indicates that this drawing was a gift from Lessitzky to J.J.P. Oud, the Dutch architect who happened to have been born the same year.
This is perhaps Lissitzky's best-known graphic design, the merged heads being a clever but not particularly meaningful touch. The event was a Russian exhibition, presumably of architectural and graphic designs.