Jos Buttler, who impressed for the tourists in Tuesday’s warm-up victory, scored his second successive half century, while Eoin Morgan also contributed 51 as Stuart Broad’s side posted a score of 170-5.
However, the New Zealand XI, who lost by 46 runs in the opening match, battled back and despite Broad’s late flurry of wickets, scored the winning run from the final ball of the match.
England approach the three-match T20 series as favourites but Lumb warned the tourists that they cannot afford to underestimate their hosts.
“I think it will be tight,” said Lumb.
“A lot of people have written them off, but you can’t take them lightly.
“It would be foolish to do that – they’ve just beaten South Africa in a one-day series over there. They’re a proud nation, and they’ll come really hard at us.”
Lumb added that Broad’s return to action from a heel injury has given England a timely boost, with the skipper taking six wickets in the two warm-up games ahead of their first T20 in Auckland on Saturday.
“It was good, especially for the four bowlers, to be put under some pressure,” added the Nottinghamshire batsman.
“And if it comes down to it in the main games, we’ll have had some experience a couple of times here.
“It’s great to have Broady back. His body is moving well, and he’s bowling nicely.
“He’s obviously had a few little niggles, but he’s back fit and raring to go. We’re really chuffed with that.”