It is disputed whether Mussolini met Lenin during his time in Switzerland.
According to Joshua Muravchik in Heaven on Earth: The Rise and Fall of Socialism, Mussolini
left Italy for Switzerland, home to many expatriates, where he lived
off friends and odd jobs, and, like so many other revolutionaries,
received the occasional subvention from his parents. There are
conflicting accounts about whether he encountered Lenin, who was also
in exile in Switzerland at the time.
RJB Bosworth's 600+ page book Mussolini makes no mention of the two men meeting. Nor does Simone Visconti in his 32-page chapter A Romagnol in Switzerland: Education of a Revolutionary (in Mussolini 1883–1915).
However, Mussolini did know Angelica Balabanoff, a
close disciple of Lenin’s, who had moved to Italy and was then
carrying out socialist agitation among Italians in Switzerland.
so a meeting cannot definitely be ruled out as the times they were in Geneva appear to overlap: Mussolini was in Switzerland sometime before July 1902 to December 1904, spending time in Berne, Geneva (from where he was expelled in 1904) and Lausanne. Lenin was there from 1903 to 1905, living in Geneva (but spent at least some of that time outside Switzerland).
The Traces of War website article on Mussolini says that Mussolini
talked to the Russian Communist leaders Lenin and Trotsky
but does not directly cite the source for this so it's hard to comment on the reliability. The 1940 edition of John Gunther's Inside Europe is the (less emphatic) Wikipedia source for this 'reported' meeting. Gunther wrote:
Mussolini, a bricklayer, apparently met Lenin through Balabanov.
This source also alludes to the Lenin quotation cited by the OP, saying
Years later Lenin rebuked the Italian socialists for having "lost"
Mussolini, their best man.
What is clear from practically every source is that Mussolini spent most of his time with Italian socialists.
While Mussolini was clearly an admirer of Lenin, he also criticized him. Roger Kimball notes in his review of Muravchik book,
Mussolini began as a disciple of Lenin and did not so much repudiate
Marxism-Leninism as become a self-declared “heretic.”
Although Mussolini initially welcomed the Bolshevik Revolution, he was soon condemning Lenin as a "traitor" for undermining the Russian army's fight against the Central Powers and for signing the March 1918 Treaty of Brest-Litovsk.
Nonetheless, during the November 1919 Italian election campaign, Mussolini referred to himself as the "Lenin of Italy" and
British journalist George Slocombe, who interviewed Mussolini at the
1922 Cannes conference, reported that “Lenin was the only contemporary
for whom he would express respect.”