Oh man, I feel for ya! Good that you've kept your sense of humour (I got the willies along with a chuckle from the "cooked lettuce" idea).
Honestly, though, I eat very few raw vegetables. I don't have your allergies, but have found that my system tolerates cooked vegetables better. To accommodate this, I tend to cook up large batches of roasted mixed vegetables (broccoli, cauliflower, brussels sprouts, carrots, parsnips,squashes, etc.) and then keep them in the fridge - my "salad" is often a big bowl of these with some home-made dressing. I find that shredding cooked brussels sprouts works well as my "greens", or I will nuke some baby spinach for a minute or so (that's long enough for it to be ok for me - not sure how that would work for you).
One of my favourites is actually sauteed shredded cabbage. I throw in some shredded onion and some hoisin sauce, along with some protein (usually shredded chicken and / or an egg) and I think it's really good. I frequently add spinach to this, too, as it sautes well.
A really fast and simple meal with a few servings of vegetables is starting with sauteing onions, mushrooms, zucchinis, and chopped tomatoes in olive oil, adding a splash of red wine vinegar and some spices (basil, sage, oregano, garlic) and then throwing a couple of fillets of cod on top (5-7 minutes per side). This is another one that I'll sometimes add spinach to, or I'll steam some brussels sprouts since the tomato/onion/red wine vinegar mix tastes great with it.
Fruits are going to be a bit trickier, depending on how long they have to be cooked for you. I quite often eat an apple or pear that has been sliced, sprinkled with cinnamon, and nuked for one to two minutes. Any berries or cherries or really juicy fruits (peaches or kiwis spring to mind) can be cooked in to a sauce (add a little wine or brandy to a saute pan, throw in the berries and cook as long as you like - lots of recipes out there) that can be added to your plain yogurt, or poured over meats (cherry merlot sauce over cocoa-encrusted pork is divine!).
You definitely have to do a bit more pre-planning and give yourself some extra time for cooking, but doing batches of roasted veggies (or steamed, if you prefer) can make it almost as easy for you to incorporate these in to your days as it is for those without your allergy.
This is a condition that definitely requires the input of a medical doctor and a dietitian.
Have you seen an allergist to see if they can determine exactly what it is that you are reacting to? The reason I ask is that I know someone who cannot eat any vegetables raw, but can eat most of them if they are cooked (I can't remember exactly what it is that she reacts to, but it's broken down by the cooking process). Hopefully, your reaction will be to something similar and you may be able to have some cooked vegetables or fruits. This is, however, something only an allergy specialist can work with you to determine.
That really needs to be your first step, and then a referral to a dietitian who is aware of the limitations and can make specific suggestions. Since most of us get the a lot of our vitamins and minerals from fruit and veggies, you should also get a blood panel done including all vitamins / minerals / electrolytes to determine if you have any deficiencies and will require supplements.
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