I've first heard of that quote in French ("La confiance n'exclut pas le contrôle"), so I was a bit surprised when I learnt that its translation in English was "Trust is good, control is better".
Literally, "La confiance n'exclut pas le contrôle" translates to "Trust does not rule out control", which I find makes the quote quite funny partly because it sounds like a contradiction. The English translation however has none of that.
So, what translation is the most correct?
Even Wikipedia now knows that Lenin didn't say that sentence at all, or at least not in the way it was handed down.
Ute Frevert: "Vertrauen und Macht. Deutschland und Russland in der Moderne", Vortrag am 25.05.2007 im Deutschen Historischen Institut Moskau. Moskau: Deutsches Historisches Institut. (PDF) My translation.)
The language problem:
First of all, this is a problem of different languages in which a witty remark, qip or apharism is to be rendered.
The isolated quote is rendered in different languages
Trust, but verify! ("Vertraue, aber prüfe nach" (Доверяй, но проверяй) & Trust is good, control is better! ("Vertrauen ist gut, Kontrolle ist besser" Доверие - это хорошо, контроль - это лучше!) If I'd be the lector for that, in most instances I'd let both translations pass as 'yeah, good enough'. The main problem here being the different connotations and additional (possible) meanings of 'control', as Russian seems to allow both meanings perfectly well, as really does French and English, whereas in German the 'monitoring' aspect is much subdued for the 'steering' aspect.
The German Wikipedia says:
"Trust is good, control is better" is a saying attributed to the Russian politician Lenin. It means to rely only on what has been verified. The saying is not present in his works and can therefore not be proven.
However, it is proven that Lenin very often used the Russian proverb "Trust, but check" (Russian Доверяй, но проверяй - Dowerjai, no prowerjai). It is assumed that this proverb was slightly modified in some translations of Lenin's texts, since the Russian word proverjai can also be translated as "check" (kontrollieren, control) instead of "check" (prüfen, verify) [the differences really get lost in my translation.)
Now scanning through the Collected Works of Lenin, we do not find any rendering coming close - really - to this popular phrase, from mangement circles?
The closest a German quote investigator has found for this would be, in German: "Nicht aufs Wort glauben, aufs strengste prüfen - das ist die Losung der marxistischen Arbeiter." - Werke, Volume 20, Dietz-Verlag, Berlin 1971, S. 358.
The English version for this is then, in context:
The history of Russian Social-Democracy teems with tiny groups, which sprang up for an hour, for several months, with no roots whatever among the masses (and politics without the masses are adventurist politics), and with no serious and stable principles. In a petty-bourgeois country, which is passing through a historical period of bourgeois reconstruction, it is inevitable that a motley assortment of intellectuals should join the workers, and that these intellectuals should attempt to form all kinds of groups, adventurist in character in the sense referred to above.
Workers who do not wish to be fooled should subject every group to the closest scrutiny and ascertain how serious its principles are, and what roots it has in the masses. Put no faith in words; subject everything to the closest scrutiny-such is the motto of the Marxist workers.
Let us recall the struggle between Iskrism and Economism in 1895-1902. These were two trends of Social-Democratic thought. One of them was proletarian and Marxist, which had stood the test of the three years' campaign conducted by Iskra, and been tested by all advanced workers, who recognised as their own the precisely and clearly formulated decisions on Iskrist tactics and organisation. The other, Economism, was a bourgeois, opportunist trend, which Strove to subordinate the workers to the liberals.
Vladimir Ilitsch Lenin: "Collected Works", Volume 20, December 1913 -- August 1914, "Adventurism", p 365, Progress Pubishers: Moscow, 1964. (Online version: V. I. Lenin: "Adventurism", Published: Rabochy No. 7, June 9, 1914. Signed: V. Ilyin. Published according to the text in Rabochy. Source: Lenin Collected Works, Progress Publishers, 1972, Moscow, Volume 20, pages 356-359. Translated: Bernard Isaacs and The Late Joe Fineberg
In Russian this would then be
Ленин В.И. Полное собрание сочинений Том 25 ОБ АВАНТЮРИЗМЕ
Не верить на слово, проверять строжайше - вот лозунг марксистов-рабочих.
While the short quote has proven its general usefulness for the managerial wise-crack, in the writings of Lenin the closest match seems to express quite a different thing.
For a more contemplative pondering about words and meanings, it seems quite instructive to compare the Lenin quote in context to
Matthew 7:15-20 (KJV)
15 Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves.
16 Ye shall know them by their fruits.
According to the German wikipedia page on the topic, the specific phrase doesn't appear in Lenin's work but it also notes that Lenin was a fan of a similar Russian proverb that goes trust, but verify.