After the BESM came the M20 and the BESM 2 - both were mass produced from 1959 on. Compared to the computers available in the West at the same time neither were top performers. The IBM 709 for example was twice as fast and had more memory. Transistors and core memories were common on machines before they were extensively used in any Russian machines. Production problems were the main reason for the lag.
The ultimate machine in the BESM line is BESM 6 - a super computer of the day (1965). Lebedev was involved in its design and used Boolean analysis to formalize its architecture. it used an early pipeline approach and processed up to eight instructions at a time. It also had memory mapping and consisted of 60 thousand transistors and 180 thousand semiconductor-diodes.
There is of course the question of how original Lebedev's work was. At the time he was thinking about building a stored program machine in 1947 there were articles available on the ENIAC and Von Neumann's report on the EDVAC was available in 1945.
However it is unlikely that Lebedev had access to these sources. Certainly building MESM was not just a matter of copying the blueprints of Western machines - even when the Russians tried this some years later the results didn't work because of component differences.
It is possible that Lebedev did receive intelligence from the KGB and the question of the independence of the invention of the stored program computer has to remain open - but when Russia planned to catch up in computing by explicitly cloning the 360 series Lebedev was very much against it. He always believed that a Russian designed machine would be better. He didn't make a vast fortune from a computer company - but he did get the Order of Lenin - three times.