He said the experiment of allowing MPs to take part by video link should lead to a fresh examination of issues such as allowing MPs on maternity leave to work and vote remotely.
“This is the beginning,” said Sir Lindsay, 63. “We will grow the digital system and we have to make sure we get the security right on online voting. It is coming.
"In the longer term we ought to look again at who can vote and how.”
In a landmark sitting, Prime Minister’s Questions was taking place on Wednesday with just 50 MPs in the Commons chamber in order to comply with social distancing rules, and another 120 taking part by video.
Sir Lindsay was taking the Speaker’s chair while the place of Boris Johnson, who is recovering from the disease, was being taken by First Secretary of State Dominic Raab.
Sir Lindsay said MPs were keen to question the Government about PPE supplies, care home deaths and faulty testing.