I've got an email out to a media rep at the Lab and will update this post when I get a response.
Updated July 7: LANL spokesman Jeff Berger told SFR yesterday afternoon that the rumor is false. "We do not have plans for layoffs," Berger says.
What about going forward?
"If the budget necessitates layoffs, we would go there," Berger says. "But we've anticipated and experienced in recent years relatively flat budgets. That's what we continue to anticipate."