He may have influenced me in various ways. His book (or books?) covered things like grand unification at a semi-popular level. And I believe that even after more than 25 years, I still remember a sentence from that book – "prostoj prostoty něbůdět" (there won't be any simple [naive] simplicity [in the future of physics], a 2005 blog post). It agreed with my feelings and I may have used the very same quote myself.
Lev's father was a decorated participant in the Great Patriotic War. When he was 24, Lev graduated from the Moscow Engineering Institute and moved to the Institute for Theoretical and Experimental Physics. In some period, he was a student of Pomeranchuk. He defended his first degree, PhD, and professorship at ages 27, 32, 38, respectively. As a professor, he raised many successful students including V.A. Novikov (the Wess-Zumino-Witten models are named after him LOL).
I've mentioned popular books but he was an important enough guy in coining words (like Wheeler or Gell-Mann). In 1962, when he was 33, he coined the word "hadron". Note that "ἁδρός, hadrós" means "thick, robust, strong" in Greek and the adjective should be interpreted as "interacting via the strong nuclear interaction". In his 1962 conference talk in Geneva, he was very aware of the obvious need to have a new word:
Not withstanding the fact that this report deals with weak interactions, we shall frequently have to speak of strongly interacting particles. These particles pose not only numerous scientific problems, but also a terminological problem. The point is that "strongly interacting particles" is a very clumsy term which does not yield itself to the formation of an adjective. For this reason, to take but one instance, decays into strongly interacting particles are called non-leptonic. This definition is not exact because "non-leptonic" may also signify "photonic". In this report I shall call strongly interacting particles "hadrons", and the corresponding decays "hadronic" (the Greek ἁδρός signifies "large", "massive", in contrast to λεπτός which means "small", "light"). I hope that this terminology will prove to be convenient. — Lev B. Okuň, 1962This was surely a successful word. If there are leptons, there must be hadrons as well. (Quarks were not generally known in 1962.) The world's main particle collider is named the Large Hadron Collider. I don't know whether Okuň was receiving 1/3 of the royalties (but many people may prefer to send the money to the folks who invented the hardon instead). And he was an editor in a nuclear physics journal. In 2013, he left the Russian Academy of Sciences because of his disagreement with a reform.
The two most well-known papers include one paper about the gluons and charmonium by a larger group of top Russian minds; and one he co-authored with Zeľdovič and Kobzarev about the domain walls – perhaps the most important pioneering paper about the cosmology of domain walls and their links with discrete symmetries. He wrote the book "Leptons and Quarks" (note that there are modestly no hadrons in the title). It may look like the book that I read but I don't remember the title! ;-)
Look at other well-known writings by Okuň (or his papers at INSPIRE). Cosmological bubbles, CP-violation, extra generations, neutrinos, and electric dipole moment corrections are among the themes, a rather modern stuff for a man born in 1929.
In 2001, Michael Duff, forefather of string theory Gabriele Veneziano, and Lev Okuň published a trialogue on the number of fundamental constants which was a reconstruction of their 1992 discussion on the terrace of CERN's cafeteria. As I explained in 2009, Okuň presented the viewpoint on the parameters and dimensionful and dimensionless constants that I fully shared while Veneziano seemed utterly confused about things that seem totally basic to me.