This is a very interesting question.
Lenin studied at Kazan, but was ultimately awarded his degree from Saint Petersburg. He was expelled after a very brief time at the University for his revolutionary activity, concurrent with many student protests across the country, which is going to make it difficult to say what exactly he was formally educated in at Kazan. It wasn’t actually until he returned to the city of Kazan, but not the university, that he would be introduced to Marx via Nikolai Fedoseev, who also mentored Gorky; Lenin’s activism at the time was focused more on his participation in the Samara-Simbirsk Zemlyachestvo that was banned. Zemlyachestva are community groups that have been implicated in quite a number of radical movements in Russia, including his brother’s circle at Saint Petersburg.
A very important aside here is that Lenin’s older brother Sasha was executed in 1887 for an assassination attempt on Alexander III; Anna Ulyanova’s biography of the family has a large emphasis on him. There is some confusion on what exactly occurred and how Lenin responded to it; purportedly he rejected terrorism as a political tool, but this is somewhat questionable. Early Soviet histories tend to present very particular, polished stories - Trotsky questioned his characterization of the young Lenin.
Lenin sat the Petersburg exams but had never studied there. So, returning the question of what exactly a late-19th century Russian education in law would look like, we can turn to A.N. Naumov’s memoirs, published abroad, that speak to his time at Moscow.
Of the protests of November 1887 mentioned above, Naumov writes
University life was completely disrupted. The lectures stopped. The professors themselves split into two camps: one was for concessions and for taking measures for the peaceful settlement of disorder, the other - for the strict application of the most decisive and repressive measures.
In all the University cities, the same thing was happening almost as in Moscow...(42) source
And of legal education itself:
The Moscow University of my student days was famous for its outstanding composition of professors and, in particular, for the Faculty of Law…[political economy and statistics, financial law, Roman law, and ecclestical law].
The basic subjects of the first year were: history of Russian law, history of Roman law, political economy and encyclopedia of law.
In the second year: Roman dogma, state law, financial law, Church law, statistics and the history and philosophy of law.
The third and fourth courses covered: criminal law (substantive and procedural), civil law (also substantive and procedural), international law, police law, commercial law, and a range of optional subjects: prisons, forensic medicine, etc. You could hear theology in any course. (44)
So hopefully that gives you an idea of what Lenin would have been examined on at Saint Petersburg. Unfortunately, a letter by Lenin says very little on the topic:
I was born in Simbirsk on April 10, 1870. In the spring of 1887, my elder brother Alexander was executed by Alexander III for an attempt on his life (March 1, 1887). In December 1887, I was arrested for the first time and expelled from Kazan University for students’ disturbances; I was then banished from Kazan. source
As does his biography by Nadezhda, though she praises his competence as a lawyer. However, Lenin did believe that “it's better to fear lawyers and not trust them, especially if they say they're social democrats and members of the party” ((30))[https://www.jstor.org/stable/pdf/2501118.pdf?refreqid=excelsior%3A6b5a3245876362152f5fb7e6c63ea45c], so lawyers in general weren’t particularly well-regarded. Not that they are today!
There are other characterizations of law that are similarly uncharitable; though there are plenty, the one that comes to mind is Leo Tolstoy, who wrote about his experience as a law student (incidentally also at Kazan, in the 1840s) in a letter from 1909, a few years before his death. Tolstoy writes
The ethical educational meaning of "law"! It's terrible. The main reason for the immorality of the people of our Christian world is this terrible fraud, which is called "law", and they talk about the educational meaning of law…” and We see how the people are being corrupted before our eyes [with crimes]... probably justified by "law"... The corrupting influence of activities based on “law” is especially noticeable now in Russia… source
I recommend James White's Lenin, particularly “The Making of a Revolutionary,” Anna Ulyanova's biography, and Nadezhda Krupskaya’s biography to look a little into Lenin’s early life.