"At this level it is about being consistent and what Lauren has managed to produce over the last 14 days is sheer consistency. We never mentioned world records coming into these competitions because she has improved so much that you do not know what to expect," Lyles said.
"It was so fast and such a big improvement (the 800m and 400m freestyle in Eindhoven) that to do it again a couple of days later is tremendous and a real credit to her."
Boyle will take a few days off before returning to New Zealand for a break and then reset her goals towards next year's Commonwealth Games in Glasgow.
Earlier fellow New Zealand teammate Shaun Burnett was 15th fastest in the 100m butterfly in 54.25.
Day 2 results, FINA World Cup, Berlin:
Women's 400m freestyle, heats: Lauren Boyle (NZL) 3:59.84, 1; Belmonte Garcia (ESP) 4:02.92, 2; Lotte Friis (DEN) 4:04.04, 3.
Final: Garcia 3:54.52, 1 (World Record); Boyle 3:55.31, 2; Melanie Costa (ESP) 3:58.31, 3.