Praise be to Allah.
The basic principle is that webmasters put this material on their websites for people to listen to it and benefit from it. Some provide the means of downloading and recording them, so this is regarded as permission from them to copy them.
Based on this, there is nothing wrong with downloading these lectures and recording them and distributing them to the youth and others, rather this is a beneficial and righteous deed, because it is calling people to Allaah and cooperating in goodness. The Prophet (peace and blessings of Allaah be upon him) said: “Whoever calls people to right guidance will have a reward like that of those who follow him, without that detracting from their reward in the slightest. And whoever calls people to misguidance will have a burden of sin like that of those who follow him, without that detracting from their burden in the slightest.” Narrated by Muslim, 2674, from the hadeeth of Abu Hurayrah.
It is not permissible to try to download lectures from sites that do not allow that, because that is transgressing against the rights of others who have written, compiled, invented etc (i.e., copyright); these are rights that are protected, as it says in the statement of the Islamic Fiqh Council issued during its fifth conference held in Kuwait, 1-6 Jumada al-Awwal 1409 AH/ 10-15 December 1988 CE:
Firstly: trade names, company names, trademarks, writings and inventions are all the copyright of their owners or authors, which in modern practice have acquired monetary value. These rights are respected by sharee’ah and it is not permissible to transgress against them. Copyright of authors and inventors is protected in Islam.
Thirdly: the owner of these rights has the right to dispose of them and no one should transgress against them.
And Allaah knows best.