Speaking in Brixton at the launch of his leadership campaign on Friday morning, Lewis said: “We are a democracy. I’d rather see us as citizens rather than subjects.”
He added: “Why not have a referendum in this country on the future of the royal family?
Lewis later tweeted: "In response to my comments about the royal family. I didn’t say they should be abolished, I have lots of respect for the hard work they do.
"I simply think the question about their size and the money they receive should be one for the public. Asking these questions is democratic."
Harry and Meghan released a bombshell statement on Wednesday which stated the couple will be “stepping back” as senior royals and will divide their time between the UK and North America.
The couple had only recently arrived in the UK after spending an extended festive break in Canada. The duchess is now back with baby son Archie who remained behind.
A conference call between the Queen in Sandringham, Charles in Birkhall, Aberdeenshire, William at Kensington Palace and Harry at Frogmore Cottage in the grounds of Windsor Castle has been staged to discuss the crisis, according to reports.
Lewis is seen as an outsider in the race to succeed Jeremy Corbyn, with Keir Starmer and Rebecca Long Bailey leading the pack.
Candidates have until Monday afternoon to secure the support of the 22 MPs required to make it onto the ballot.
Lewis currently only has four supporters, but around 50 Labour MPs have yet to formally endorse anyone.