The top seed and home favourite, who had never made it beyond the second round in Gstaad, disposed of Lisnard decisively in front of a sell-out 6,000 crowd.
Federer will next face Spaniard David Sanchez who knocked out defending champion and seventh seed Alex Corretja 6-4, 6-4.
Federer, now ranked third in the world after becoming the first Swiss male Grand Slam winner at Wimbledon on Sunday, struggled to adapt to the clay courts high in the Alps on Tuesday when he scraped past Spanish qualifier Marc Lopez.
But the 21-year-old from Basel rediscovered his Wimbledon form with a commanding performance against unseeded Lisnard.
"The game went perfectly for me and my serve was excellent all of the time - just like Wimbledon," said Federer, who won seven games in a row and took only 53
Federer beat Sanchez in four sets in the French Open third round two years ago.
"Playing Sanchez will not be a simple task," Federer said. "I have already had some trouble against him on clay."
Corretja, who has won the clay court event three times in the last five years, lost in the opening match of the day as his poor recent form continued.
Corretja had not initially entered the Gstaad tournament because his wife was due to give birth on July 4, but was handed a wild card after his daughter Aroa arrived early.
Second seed Rainer Schuettler of Germany, the Australian Open finalist, set up a quarter-final against Czech Radek Stepanek, seeded eight, after both came through their second round games unscathed.
Schuettler saw off Belgium's Christophe Rochus 6-3, 7-6, while Stepanek overcame Switzerland's Michel Kratochvil 6-3, 7-6.