Short answers, pulled from the story.
Lev Shestov was a Russian existentialist and religious philosopher born Yeguda Lev Shvartsman in Kiev, who lived from 1866 to 1938. He is best known for his critiques of philosophical rationalism and positivism, arguing that reason cannot conclusively establish truth about ultimate problems such as the nature of God or existence. Contemporary scholars associate his work with the label "anti-philosophy."
Athens and Jerusalem, written between 1930 and 1937, examines the dichotomy between freedom and reason and argues that reason should be rejected in philosophy. The book contends that the scientific method has made philosophy and science irreconcilable, since philosophy must concern itself with freedom, God, and immortality, issues that empirical observation cannot resolve. Leo Strauss later wrote his essay "Jerusalem and Athens" partly in response to Shestov's book.
Albert Camus wrote about Shestov in Le Mythe de Sisyphe (The Myth of Sisyphus). Gilles Deleuze referred to Shestov in Nietzsche and Philosophy and Difference and Repetition, and Shestov's ideas on thinking beyond logical limits influenced Deleuze's philosophy. Emil Cioran called Shestov "the philosopher of my generation" in his collected works published by Gallimard in 1995, crediting Shestov with recognizing that the true problems of life escape academic philosophy.
D. H. Lawrence wrote the foreword to S. S. Koteliansky's English translation of All Things Are Possible and summarized Shestov's philosophy as centered on the cry "'Everything is possible.'" Lawrence specified that this was not nihilism but "a shaking free of the human psyche from old bonds," with the positive idea being that the soul believes in itself and nothing else.
Shestov left Russia after the Bolshevik seizure of power in 1917 made life difficult for him. The Marxist authorities pressured him to write a defence of Marxist doctrine as a preface to his work Potestas Clavium, threatening to block its publication if he refused; Shestov refused. He eventually settled in Paris in 1921, where he lectured at the Sorbonne in 1925 and became a prominent figure in French intellectual circles.
Shestov was introduced to Kierkegaard in 1929 at Husserl's urging and recognized strong similarities with his own thought, including rejection of idealism and distrust of objective reason. He concluded, however, that Kierkegaard had not pursued his own insights far enough, and continued where he believed Kierkegaard stopped. The result was Kierkegaard and Existential Philosophy: Vox Clamantis in Deserto, published in 1936 and considered a foundational work of Christian existentialism.