US citizenship required. And: 'If you hold multiple citizenships (U.S. and another country), you may be required to renounce your non-U.S. citizenship before a DOE L or Q clearance will be processed/granted.'
The lab clears basically all salaried employees at L or Q; if there's any chance that you might look at classified data some day (IE: if you want to interview at another group internally, or have some useful expertise that can be leveraged somewhere else), it saves everyone time and energy if you're already a Q. There's some financial reasons not to do it, but I think the math works out in favor of not running multiple levels of background check on every new hire (if they were to give you an L and then a Q).
I worked at LLNL 2001-2005 as a mechanical engineering. It was a very nice place to work. I had to go through the clearance process and that was the weirdest part. They sent people to interview a camp councelor I had when I was 10 years old! I also had to list every address I had lived at and every country I had ever visited with cooresponding dates.