According to CNN and Brian Fallon, Hillary Clinton's former press secretary, Donald Trump had less viewers witnessing the Inauguration than press secretary Sean Spicer indicated and are calling for Trump's press secretary to step down for lying during the first press conference.
According to CNN
History of Inauguration Viewers on Cable Television
Trump's Viewers of 2017 Inauguration
But Wait.... How About Online Live Stream?
Facebook Live Launched April 2016. But Wait...
How About Every Media Site Offering Live Feed From Apps and Websites?
Conclusion: Trump and Spicer weren't lying and did in fact have the most viewers of any Inauguration ever, if you count real viewers and not just cable television.