My last rabbit had fur that came out like dandelion fuzz so she was very pluckable which made for easier and yet much more hairy shedding season. For a bunny that just sheds in full on 'cloud of fur' though - I've seen some gloves online that you wear and stroke the rabbit. Maybe those would help? We used to have a trick for the family cat that I'm not sure might or might not work on a rabbit but we'd take a mild tape - like that blue painters tape - something without a lot of cling to its stick and we'd wrap it around our hand sticky side out and pat and stroke the cat. He didn't seem to mind and like I said you don't want tape that's actually going to stick to the animal itself so much as something that will just pick up the loose hair. We never got the tape stuck to the cat so it worked for him. Not sure if that kind of thing would work for your bunny and you or not. You'd have to very carefully experiment so Lulu didn't end up running off with your hand but it might be worth a try?
Depending on where you are - I lived near a rabbit breeder for a few years and she'd come over and shave Fizz a couple of times each summer for me for a small fee. In Fizz's case it was to keep her cool during the hot months but maybe something like that if available might help with the shedding too?