The fly-half played for Wellington against the Lions in 2005, and has been instrumental in Wasps' charge to the top of the Aviva Premiership.
"I'd be going out there looking to run them off their feet," he told the Rugby Union Weekly podcast.
"I think you go there with an attacking mindset," added the 33-year-old.
The Lions visit New Zealand from 3 June to 8 July, with a three-Test series taking place on the last three Saturdays of the tour.
"Even if it's wet, the pitches are like cricket grounds, and the way you see the guys playing in the Premiership and Pro 12 - the skill level [they have] - I would be picking a team for all-out attack," concluded Gopperth.
Gopperth faces his old side Leinster in the European Champions Cup quarter-final this weekend, as Wasps look to reach the semi-finals for the second year in a row.
Usually an outside-half, Gopperth has played at inside centre this season with Danny Cipriani at number 10, and he feels this two playmaker approach is a necessity in the modern game.
"Back at home in New Zealand it started a long time ago," he said.
"Even when Dan Carter was coming in, Dan would play 12 with Andrew Mehrtens at 10.
"It just adds a lot more to your game, it adds a lot more width, and it asks a lot more questions of your defence.
"It varies your attack and puts teams under a lot more pressure."
Wasps' trip to Dublin comes just a fortnight after England were denied a Grand Slam by Ireland.
The likes of James Haskell, Joe Launchbury and Elliot Daly return to the Aviva Stadium to face a Leinster side packed with Irish internationals.
"You can't afford to make errors in these big games," Gopperth added.
"If you play the best you can [individually], then collectively we have the goods to do the job.
"It's knockout rugby, it's where you want to be. The Aviva Stadium is outstanding - a brilliant surface, a brilliant atmosphere - so all the cards are lining up for it to be a really good afternoon."
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Listen to commentary of Leinster v Wasps and Saracens v Glasgow in the Champions Cup this weekend on BBC Radio 5 live sports extra.
The British and Irish Lions must adopt an "all-out attack" approach in New Zealand, says Wasps' Kiwi playmaker Jimmy Gopperth.