Resuming from their overnight score of 203 for five, the tourists lost their last five wickets for 46 runs as Lakmal dominated.
Ross Taylor was dismissed for 86 on his first delivery of the day as he attempted a casual cut shot to a harmless Lakmal delivery and was caught behind.
Mitchell Santner then shouldered arms to a Lakmal ball that nipped back and was trapped leg before wicket for 13.
William Somerville was given caught bat-pad to Akila Dananjaya but he successfully overturned the decision after a review to deny the off-spinner his sixth wicket.
Tim Southee's promising innings was cut short when he was run out on 14 attempting a suicidal single.
Lakmal then removed Trent Boult and Ajaz Patel in successive deliveries to finish with figures of four for 29. He will be on a hat-trick when New Zealand resume their second innings.
New Zealand will be disappointed with their batting display as most batsmen got off to starts but failed to convert them into big scores.
Play resumed 15 minutes early on Thursday after 22 overs were lost on day one due to rain. A total of 98 overs are expected to be bowled on Thursday, although rain is predicted after tea.