New Zealand will be looking for BJ Watling to stretch New Zealand's lead beyond 200 when they resume on day four.
Jofra Archer was among three wicket-takers in the morning session, reducing Australia to 80-4 at lunch before rain ended play on day three.
The West Indies batsmen will be able to tap into the knowledge of Brian Lara and Ramnaresh Sarwan ahead of two Tests against India.
BJ Watling raised hopes of New Zealand winning the first Test after Sri Lanka had the tourists in the mire on Friday.
Rory Burns is looking forward to England "getting their own back" with the ball after Australia's aggressive bowling at Lord's.
Australia spinner Nathan Lyon plays down matching Dennis Lillee for Test wickets, saying: "I'm just some guy trying to bowl off-breaks."
Josh Hazlewood was left out of Australia's win at Edgbaston in the first Ashes Test but he made the most of his recall at Lord's.
England were 201-6 at tea on day two of the second Ashes Test at Lord's as Australia took advantage of winning the toss.