Promote Lucy to "Crew Chief" - she can oversee rations and be the "lead dog" in the welcoming committee when you pick up your time slip.
I don't know that there's a formal rule on this, but I doubt they'll let you race with a navigator. The officials and safety folks aren't prepared to be pulling two mammals out of a car. You'll need to concentrate on keeping it between the mile markers, and God forbid something happened, you'd never forgive yourself if Lucy got hurt.
Regarding Lucy - even with booties, it's a tough environment for a canine. I'd bring along a dedicated rug or blanket that she can stand on, and try to keep her in the shade. You'll want to keep a close eye on her out there. Even with the booties, she'll be licking her paws, and ingesting more salt than normal.
Personally, I wouldn't bring a dog, but I understand the familial bond that pets bring to the relationship.
I saw about a dozen pet owners at Speedweek this year with their dogs in tow - perhaps someone who has brought a dog on the salt might have some advice they'd share.
Have fun - the USFRA does a great job with this event.