Mr Lewis's clients include the family of murdered schoolgirl Milly Dowler.
He is also taking legal action over revelations the News of the World hired investigators to follow him and members of his family.
The parents of missing girl Madeleine McCann, Sheryl Gascoigne - former wife of ex-footballer Paul - and journalist Tom Rowland are due to appear later.
Mr Lewis took out injunctions on behalf of former footballer Garry Flitcroft, who gave evidence to the inquiry on Tuesday, and later Jo Armstrong, a legal adviser at the Professional Footballers Association (PFA).
He said he took out an injunction over a photo taken of Ms Armstrong and PFA chief executive Gordon Taylor by the News of the World. Mr Lewis said it was only after he managed to block the publication of the photo that he had a "eureka moment" and realised that the only way the paper could have got the accompanying story - which was untrue - was through phone hacking.
"It just wasn't a proper legitimate investigation.... A phone had been hacked in order to get this story."
Mr Lewis said that Ms Armstrong had left a message on Mr Taylor's phone thanking him for speaking at her father's funeral.Continue reading the main story
Leveson Inquiry: News Int complaint re Guardian article. Barrister says SUN didn't doorstep one of Inquiry's barristers.”End Quote Analysis Peter Hunt BBC correspondent, at the inquiry "The tabloid journalist who listened, knew of that message, added two and two and made 84. If it hadn't been so sad it would have been funny."
Mr Lewis represented Mr Taylor in a civil case against News Group News - a subsidiary of News International, which owned the News of the World. He said News Group News eventually paid Mr Taylor's legal costs plus £425,000 in damages.
Mr Lewis said the News of the World had been the focus of the phone-hacking row because private investigator Glenn Mulcaire had written things down but that evidence from his clients inferred other news organisations also illegally accessed phones.
"It was a much more widespread practice than just one newspaper," Mr Lewis said.
The hearing opened with discussions on a supplementary statement submitted by Mr Lewis said to pertain to Article 8 of the European Convention on Human Rights.
Lord Justice Leveson suggested that the lawyer's second statement be the focus of a later hearing and that private discussions take place about how its information should be treated.
Derek Webb, who ran private investigations firm Silent Shadow, told the BBC earlier this month that he had been commissioned by the News of the World to carry out surveillance on Mr Lewis and his former assistant, Charlotte Harris, in early 2010.
News International, which owned the now-closed newspaper, said the action was "deeply inappropriate" and "not condoned by any current executives".
Lord Justice Leveson's inquiry is looking at the "culture, practices and ethics of the media" and whether the self-regulation of the press works.
Prime Minister David Cameron established the inquiry in July after it was revealed that Milly Dowler's voicemail may have been hacked while she was missing.
A second phase of the inquiry will commence after the conclusion of a police investigation into NoW phone hacking and any resultant prosecutions. It will examine the extent of unlawful conduct by the press and look at the police's initial hacking investigation.