Don't know any recipes for mayo, with or without eggs. BUT did you know that you can drink buttermilk or use it in cooking? (I figured anything with milk in it was off-limits until I found that out.)
Also, yoghurt is OK too, as long as it contains active lactic cultures. Not all of them do, however.
If it has acidopholus (sp?) on the list of ingredients, it is fine.

Eggless Mayonnaise - vegweb.com

3 tablespoons lemon juice
210 ml soya milk
1/4 teaspoon salt
1/4 teaspoon paprika
1/4 teaspoon prepared mustard
6 tablespoon vegetable oil
Directions:

Put all the ingredients except the oil in a blender. Blend on the lowest speed. Gradually - literally one drop at a time - add the oil until the mixture starts to thicken. Continue blending until thickened and smooth. Transfer to a jar and store in the refrigerator.

Soy Mayonnaise - vegweb.com

12 ounces firm tofu
6 tablespoons oil
1 tablespoon cider vinegar
1/2 cup water
1-1/2 teaspoons prepared yellow mustard
4 tablespoons minced onion
1 teaspoon minced garlic
1/4 white pepper
1-1/4 teaspoons sea salt
1 tablespoon lemon juice
1 tablespoon very finely ground cashew nuts (optional)
Directions:

This is a basic, all-purpose mayonnaise that will keep, refrigerated, for 8 to 12 weeks. If you are using the cashew nuts, make sure that they are ground until they turn into a fine meal, or your mayonnaise will feel gritty. The same mayonnaise, with garlic, onion and mustard omitted, may be used for fruit salads. Place all ingredients in a blender and blend until smooth and creamy. Refrigerate until cool. Makes 2-1/2 cups of mayonaise.

Serves: 20 Preparation time: 15 minutes

Here is a link that might be useful: Tuna Salad/Sandwich from Vegieworld.com

Another recipe for mayonnaise to make tuna sandwiches with:

All-Tofu Mayonnaise
From: This Can't Be Tofu! by Deborah Madison
(Bantam Doubleday Dell; April 2000; ISBN: 0767904192; Paperback)
Cookbook Heaven @ Kitchenlink.com

Here's an all-tofu mayonnaise, but your family may never suspect, especially if you add a tablespoon or more of prepared mayonnaise a good idea if you're nervous about it. (Although this option is not for you, Kitty.) This will keep, refrigerated, for up to five days.

Makes: about 1 cup

6 ounces soft tofu, well drained, or 1/2 box silken tofu
2 tablespoons prepared mayonnaise (optional)
1/3 cup olive oil
1 small garlic clove
2 teaspoons Dijon mustard
2 1/2 teaspoons fresh lemon juice or vinegar (red or white wine)
Salt and freshly ground white pepper

1.Put the tofu in a food processor with the mayonnaise, if using, and oil. Puree until smooth.
Scrape down the sides.
2.Add the garlic, mustard, lemon juice, and 1/4 teaspoon salt, and puree until smooth. Taste
for salt and season with a little pepper. Scrape into a bowl and refrigerate until ready to use.

Variations:
Mustard Mayonnaise: Increase the mustard to 4 to 5 teaspoons, or to taste.
Garlic Mayonnaise: Coarsely chop 4 to 6 cloves unblemished garlic. Pound in a mortar with 1/2 teaspoon salt until the garlic breaks down to a smooth puree, then stir it into the mayonnaise.
Saffron Mayonnaise: In a small mortar, grind 2 pinches saffron then cover with 1 tablespoon boiling water. Let steep several then stir it into the mayonnaise.
Pepper Mayonnaise: Puree 1/2 cup roasted peppers until smooth with 1 garlic clove and a pinch of cayenne and add it to the mayonnaise.
Mayonnaise with Capers and Fines Herbes: Stir into the mayonnaise 2 tablespoons rinsed capers, 1/4 cup chopped parsley, 2 tablespoons each chopped tarragon and snipped chives.
Chlpotle Mayonnaise: Add 1 teaspoon pureed chipotle in adobo sauce into the mayonnaise. Taste and add more if you prefer it hotter. In place of lemon in the mayonnaise, use fresh lime juice.

Go to any decent sized health food store (or even a large supermarket) and you will find Nayonase, looks like mayo, smells like mayo, tastes like mayo, but is vegan (no animal products)! It's healthy too.

Why is Buttermilk ok when you are lactose intolorant? Thats nice to know since I wanted to make a cake with the ingredient, but what about other recepies? My fiance doesnt do milk products at all, period. Mayo, eggs, & butter are ok in small amounts, but I'm finding it rather hard to bake (my passion) or even cook some dishes that he can enjoy with me.

Please help!

bugz

Don't know why buttermilk is OK. Probably for the same reason that butter is OK (in small amounts) - because it doesn't have much lactose in it. For example, the more aged a cheese is, the less lactose it has in it too.
P.S. Eggs don't have any milk in them.

Thanks Jane, I know eggs don't have milk in them......:-) but that seems to be something else he has a problem with, but in small amounts its ok.

bugz: Sorry for being snotty about the eggs - I've been short-tempered these last few days (am in the middle of wedding preparations and suffering from lack of sleep as well as too much "good advice").
Has your fiance (or you as cook) tried egg whites only? Egg yolks bother a couple of people I know, but not egg whites.

Is he allergic to milk - that is, the protein in milk, or is he "just" lactose intolerant. (There are pills to take if he is lactose intolerant and a special lactose-reduced milk.)
There are also one or two margarines available that do not contain any dairy products, which you could substitute for butter.

bugz: If your fiance is allergic to the proteins in milk, soymilk could be used as a substitute for milk. I expect the substitution is one for one, but I don't know anything about what the change in taste is like. (I'm "only" lactose intolerant.)

Soy milk works out exactly the same as normal milk in baking... but if I'm making a cake or something that's not custardy I'll use fruit juice and it's nicer, or for a savoury pastry I use plain water becuase I wasn't using enough soymilk and I was wasting most of the carton...

There are several dairy-free margerines on the market and they cook exactly the same as the standard type. Nuttelex is one of them, and I've just started using Naytura soy margerine and I like it better.

I'm afraid I can't help you on the egg front though...

Karen

PS. For other baking ideas try looking up Pritikin stuff... I've bought some sugarless, eggless, dairyless, wheatfree pritikin fruit cake at the healthfood shop and it wasn't bad.