After seeing his new charges pegged back by a late goal in a 1-1 midweek draw against Bohemians, Lampard enjoyed his first win since taking the reins as head coach nine days earlier.
Giroud's brace equalled the number of Premier League goals he scored for Chelsea in 2018-2019, while Mount's lively performance will have come as no surprise to Lampard, who managed the 20-year-old during his loan spell at Derby County last season.
Michy Batshuayi, who scored against Bohemians, impressed again in the early stages at Richmond Park, where he crashed a shot against the crossbar after 14 minutes.
Moments later, Mount latched onto Mateo Kovacic's well-timed pass and rolled the ball calmly into the net.
Ross Barkley hit the post for Chelsea before Emerson Palmieri's long-range strike slipped through goalkeeper Barry Murphy's hands and into the net.
Just before the hour Giroud met Kenedy's cross with an unstoppable volley, beating Murphy at his near post, and the France international netted again two minutes from the end to send a message to his new coach ahead of the season.