This technique works best if you buy your lettuce or cabbage the day before you intend to use it but it's probably possible to get good results on the same day if you give it enough time, it's just that I've never tried it. There are a couple of caveats: it will only work on vegetables that are reasonably fresh, the technique involves rehydrating the leaves (yes I know they seem soggy but they've actually dehydrated) if their not sufficiently fresh it wont work because the cell membranes with have broken down, so don't try it on that week old cabbage. The next caveat concerns hygiene, you're rehydrating the leaves, so you must take steps to ensure that water you use is safe to consume, this is especially important with uncooked vegetables. So be scrupulous in ensuring the utensils you use are clean as well.
Step one: wash your vegetables thoroughly then give them an extra rinse.
Step two: now steep them in clean water for a couple hours, preferably cool water in cool conditions. You can change the water periodically if you wish.
Step three: remove your vegetables from the water and place them in a closed but unsealed bag, do not remove excess water from your vegetables.
Step four: place the bag with the vegetables in your fridge and leave there overnight.
That's it -- all you need to do now is open your fridge the next morning to retrieve your vegetables, that are now crisper than those packets of Golden Wonder that always to seem to materialise behind you, just as you've settled into your seat in the cinema. Don't ask me how it works, I haven't the faintest idea beyond it's obvious that the leaves are being rehydrated but I'm not sure why it shouldn't be apparent immediately you remove them from the water. Obviously if you leave 'em in the fridge for too long they'll probably go all droopy again, so it's probably best to consume them within 24 hours. Incidental it's also worth doing this with cabbage if it's a bit droopy and you intend to cook it, it improves the texture a lot. I only cook green cabbage myself and that does tend to suffer from droop more than the white stuff but you could try it with that too.