Seems like it's going to be about a race against the clock rather than limited lives—as there's no indication I can see of any life meter. Another possibility is that there's some other penalty for death beyond time lost and/or the revive mechanic from campaign is involved.

Going to be great fun leveraging all the REQ sandbox on some AI opponents.

The press release: http://news.xbox.com/2016/03/20/first-look-at-warzone-firefight-in-halo-5-guardians/