Where there's life there's hope. Newborns can take a lot of chilling, every experienced rabbit breeder has had at least a few "Lazarus babies!" Warm them up gently. Sometimes, trying to get them too warm too soon can cause them to seem to revive and then crash, but it sounds like you are doing the right things. I have a friend who has been known to tuck chilly buns in her bra to warm them up!
Newborn kits are amazingly mobile, so that they were everywhere is not surprising. If they didn't get stepped on or otherwise injured, they have a good chance of making it, once they get warmed up.
I like ack123"s advice, but if this had happened in my rabbitry, this is what I would do:
Pack a nestbox with hay (or whatever your does get for nesting material) Make a tunnel to the back, just like the doe would. If the doe has pulled any fur, collect it and put it in the back. Pull fur from the doe if you have to, I have used fur from other rabbits in a pinch (they were shedding; my does don't seem to care whose fur it is.) Put the babies in the box, and put a soda bottle full of very warm water in the box, pushed to one side. If the babies need the warmth, they will snuggle up to the bottle, when they don't, they will move away. Keep checking, don't let the bottle cool down enough to chill the bunnies (make sure you got the cap on tight, too!). Check the corners of the box, make sure that none of the babies have crawled so far away from the others as to get chilled again. Within a couple of hours, if there are enough buns (at least 4) they should be able to keep each other warm, if you have them in the house.
I have had a few does that I had to teach to nurse their litters. Usually, I just put the box in the cage, and go about my rabbitry chores, watching to see if the doe gets in the box. If she doesn't get in there within a few minutes, I will put the nestbox into a carrier that is no bigger than the box, and put Momma in the box, and close the carrier lid. The babies usually find her, and she usually will stand and let them nurse. I have only had one doe that absolutely refused to let the babies nurse, her litter was farmed out on someone else and she was sold as a pet. Some does have had to be locked in like this for several days before they "get it," but all the others did catch on and nursed the babies like pros from then on!
I also wouldn't leave the box with the doe. Her nesting instincts may kick in late, and she may dig in the box, or she may eat the nesting material (including the fur!!) Many of my does will continue to pull fur every once in a while for several days after their litters are born (particularly in cold weather), I just collect it and add it to what is already there. Kits can get out of the box in a number of ways, it would be exasperating to lose one later, after you tried so hard to give them a chance in the beginning.
As to where this litter came from? Yes, it is entirely possible that she was bred through the wire by the mini lop. I've never seen how they do it, but I have had a couple "mystery litters" myself that can only have happened that way. Some of my cages have solid dividers, some don't, if I have to house a doe next to a buck with only wire in between, I make sure that they are both the same breed (that way, any surprises will at least be purebreds!)
Good Luck!