Broad's side lost their opening match of the tournament in Bangladesh by nine runs under the Duckworth-Lewis method, with the Black Caps being ahead of the run-rate after 5.2 overs in their chase of 173.
Flashes of lightning had been seen around the ground in the preceding minutes, but the officials did not bring the players off until five overs had been played, which constitutes a result in T20 cricket.
Broad criticised Paul Reiffel and Aleem Dar of "distinctly average decision-making" in his post-match press conference, and Lumb agrees that the players felt unsafe and should have left the field before they did.
"I think Stuart covered it in detail but, from a personal point of view, you don't mess around with lightning," he told reporters. "There are lives at stake. It was literally right above us and it was pretty scary.
"It would have been a different story if we were waking up this morning talking about guys who were struck by lightning. If we were on a golf course, we'd probably have been taken off.
"It's a serious thing and it's not to be messed with. I'd have been quite happy to go off the field [earlier]."
England and New Zealand would have earned a point each had they been withdrawn before the completion of five overs, but Brendon McCullum's six off Broad helped put the Kiwis ahead under the D/L rule.