When Lenin spoke about the press, he spoke of the resources needed to publish: paper, ink, presses, and the workers doing the publishing. It's easy in the digital age to let ourselves imagine that our publishing doesn't take up any limited resources, as it is so easy to open up a website and hit "post." But we can't forget the data storage, the bandwidth, the electricity, and all the miners, factory workers, and technicians that make this possible. So while the scale has changes, the principles have not.
The freedom of press, as MLs view it, is not the freedom to publish whatever one wants with no consequence, but rather that the workers who make publication possible be free to own their own industries, that they be free from the oppression of the capitalist ruling class. A free press is not mutually exclusive to the silencing of certain viewpoints, but the viewpoints being silenced are those of the reactionary who wish to hide the truth and oppress the masses. Information is power, and power must be taken away from those who wish to do us harm.
I see a lot of nostalgia for the "wild west" days of the internet. This, in contrast with today's homogenized corporate online landscape, is completely understandable. But we cannot forget that those days were rife with bigotry, violence, and harassment. I believe that the web has never been its best self. It was born through imperial violence, came into its own as a libertarian free for all, and now sits as a neoliberal corporate ad-revenue scam. What does a world wide web look like where truth and cooperation are king and the power lies in the hands of the people? I'm not sure, but I hope I can see it one day.