Back in 1915, a Russian named M. Osipov published a paper in a Tsarist military journal that was Lanchester like: http://www.dtic.mil/dtic/tr/fulltext/u2/a241534.pdf
He actually tested his equations to historical data, which are presented in his paper. He ended up coming up with something similar to Lanchester equations but it did not have a square law, but got a similar effect by putting things to the 3/2nds power.
As far as we know, because of the time it was published (June-October 1915), it was not influenced or done with any awareness of work that the far more famous Frederick Lanchester had done (and Lanchester was famous for a lot more than just his modeling equations). Lanchester first published his work in the fall of 1914 (after the Great War had already started). It is possible that Osipov was aware of it, but he does not mention Lanchester. He was probably not aware of Lanchester’s work. It appears to be the case of him independently coming up with the use of differential equations to describe combat attrition. This was also the case with Rear Admiral J. V. Chase, who wrote a classified staff paper for U.S. Navy in 1902 that was not revealed until 1972.
Osipov, after he had written his paper, may have served in World War I, which was already underway at the time it was published. Between the war, the Russian revolutions, the civil war afterwards, the subsequent repressions by Cheka and later Stalin, we do not know what happened to M. Osipov. At the time I was asked by CAA if our Russian research team knew about him. I passed the question to Col. Sverdlov and Col. Vainer and they were not aware of him. It is probably possible to chase him down, but would probably take some effort. Perhaps some industrious researcher will find out more about him.
It does not appear that Osipov had any influence on Soviet operations research or military analysis. It appears that he was ignored or forgotten. His article was re-published in the September 1988 of the Soviet Military-Historical Journal with the propaganda influenced statement that they also had their own “Lanchester.” Of course, this “Soviet Lanchester” was publishing in a Tsarist military journal, hardly a demonstration of the strength of the Soviet system.