Short answer: His allergy, his problem. IMHO he should be doing some of the cooking, and coming up with "safe" recipes and ingredients. I'd hope he'd already seen an allergy & nutrition specialist (can get a referral from your GP) to check what triggers the eczema and to give tips on how to get a varied & balanced diet while avoiding his triggers/allergens. There are various eczema and food allergy websites and messageboards, many of them will give advice, moral support, recipe suggestions etc.
Long answer: If you really want to be with him, it's your problem too. IMHO his food choices (for whatever reason) need to be given the same consideration as you'd like others to give your food choices. IMHO both of you need to work out whether all the food at home is to be "safe", or how you're going to keep "safe" food (and anything porous which touches it) separate from "unsafe" food so that there are few mishaps.
Thinking about the food you need to replace (citrus and tomatoes), it's mainly colour, sweetness and a bright sour note you're after, isn't it? Sour/sharp apples (granny smith or bramley) can replace sourness, so can tamarind (you can buy it as a paste if you can't be doing with soaking it & sieving out the seeds), cider vinegar, sharp/dry apple juice, barely ripe kiwi fruit, pineapple, and slightly under-ripe passion fruit. Balsamic vinegar (white or red) might also help. As others have already said, colour & bulk can be supplied by paprika, red peppers, beetroot, or finely grated carrot. You'll never replicate 100%, but you'll get near enough to have a decent meal.
Non-dairy substitutes can be pretty disappointing, but AFAIK it's possible to find vegan pesto (so little "cheese" in it that it barely ruins anything) if you want something quick & easy for pasta. Otherwise, look for recipes on the net, alter them a bit if need be, get used to cooking batches of "safe" pesto, processed untomato base, unlemon sauce etc and freeze them (split into the amount you'd add to a meal for 2).
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FWIW I've got a condition which could be serious (IME antihistamines & painkillers aren't the solution, just palliatives) unless I'm v careful about what I eat, smell and touch. That includes anyone I kiss or go down on because the trigger gets into saliva, sweat and other secretions - sorry if that's grossed anyone out - it's not easy explaining on a 1st date why even a peck on the cheek is out unless the person gargled thoroughly after eating.
Luckily it's only one family of vegetable, but it's v widely used. It's in a lot of the stuff people think of as basic ingredients (sauces, pastes, spreads, savouries of all kinds) - I end up taking my "safe" stock cubes on holiday (and a few snack bars in case there are entire meals which turn out to be "unsafe") and have learnt to check the ingredients
before eating even if I really trust the cook.
People who take it seriously make all the difference.
