England and Northampton number two Thompson will compete with Shane Byrne, Gordon Bulloch and Andy Titterrell for a starting place.
And World Cup-winning former England skipper Johnson, who retired from rugby after Leicester's Zurich Premiership final defeat by Wasps last weekend, believes Thompson should get the nod.
"I think Steve Thompson is one of the key guys for them - he needs to be in good form," Johnson told BBC Sport.
"He can do a lot of things that other players can't do in terms of his ability with the ball."
Johnson led the Lions to victory over South Africa in 1997 and also captained the defeated 2001 side in Australia.
And he added: "It would be nice to see him (Thompson) at his best, running with the ball for the Lions. It would give them another card to play."
Johnson, whose finest moment was lifting the World Cup in Australia in 2003, believes the man who kicked England to victory back then - Jonny Wilkinson - can also announce his return to the big stage in New Zealand, as well as Irish centre Brian O'Driscoll.
"Obviously Brian O'Driscoll is captain and there's a focus on him, he's an absolutely outstanding player and it would be great for the Lions if he was in his best form," Johnson continued.
"If Jonny Wilkinson is at his best he offers some things that probably no-one else there can do, particularly defensively and he's very experienced in the big pressure games.
"But certainly there are enough players there to cover anyone if they are not at their best."