Lunt showed great feet to dodge with the ball between two defenders to reach the line on 19 minutes from Eorl Crabree's final pass. The former Castleford ace then charged down an attempted clearance and dashed 50 yards for a stunning solo effort on 69 minutes.
Lunt was also involved in the game's opening try, scored by prop Crabtree, playing a new loose forward role, after eight minutes. Danny Brough, who kicked five goals in last week's 40-4 win at St Helens, converted five out of Huddersfield's six tries.
The Giants had the better of a dull first half and led 12-6 at the break thanks to the touchdowns from Crabtree and Lunt.
London, beaten 28-14 at home by last season's wooden spoonists Widnes in round one, scored through Shane Rodney's solo effort on 24 minutes.
Huddersfield moved the ball from left to right through Brough, Luke Robinson and Grix, with Jermaine McGillvary just failing to score with an acrobatic dive for the ball.
The game was then stopped on 33 minutes when Huddersfield's David Faiumu appeared to suffer a head injury in a heavy challenge. Play re-started after about three minutes, with Faiumu taking no further part in the game and Ukuma Ta'ai coming on for his debut.
Hudderfield stepped up a gear early in the second half, though Leroy Cudjoe fluffed an easy chance to score on 51 minutes. Cudjoe, who bagged two tries in Huddersfield's stunning win over St Helens, broke down the right and only had one defender left to beat. But he instead telegraphed a pass outside to the oncoming McGillvary which was intercepted.
It was only a temporary reprieve, though, as Kopczack, on his home debut, powered over and then Lunt settled the match with his solo effort.
Brett Ferres, who made a try-scoring debut at St Helens, went over and Joe Wardle powered through in overtime to complete a comprehensive victory.