Welcome,
It's aways difficult to answer a what do I need question when you'd like to make a custom light. We'll try, but you need to give us more information and show us what you're planning. It is easy for people here to look at your drawings and tell you what will and won't work and why.
So you've decided on a Zippo as the body and you want to use a Luxeon I. You are going to face some serious challenges due to your host's size and flat shape.
You asked if you should use a lambertian (high dome) luxeon. Your other choices would be a low dome (not so common anymore) or side emitter. What optics are you going to use with that Lux I? In order to turn the beam of that Luxeon into soemthing besides a flood light, you need a reflector or optic which probably won't fit in a zippo.
Also, what batteries are you planning on which are small enough to fit but have enough power to provide the light with high enough voltage (depends on the vf of the particular led you have) and sufficient current (the 350ma you've read of) for a period of time.
The luxeon certainly does require proper heatsinking, which adds furthur complication to your design. That heat is stuck in a tiny space without many places to go.
I don't want to cramp your creative energy, but this is going to be a tough job, and if you really want to squeeze a lux I in a zippo, you won't have room for good optics, good heatsinking, and good batteries.
You could stick your led to a bit of copper, wire it to a couple watch batteries, and slide it into a zippo with a hole cut in the side, but this doesn't sound like a project that will look or work particularly well. If you really want a light in your zippo, I'd recommend using 5mm leds, since you won't need optics or heatsinking. You still can't get away from the battery issue though. Then, you'd really have nothing more than a fatter version of a keychain light.
SO, perhaps you may rethink your design with a different host. Notice how most lights are cylindrical? That's because you need a lense, an optic or reflector, your luxeon, a good heatsink, either appropriate resistors or a driver circuit, appropriate batteries, some kind of a switch, and some kind of a means to hold it all together.
I'd recommend you look at some posts of how people have made their lights, and look at pictures of dissasembled lights. Flashlightreviews.com has a homemade section with instructions on various projects. ledmuseum.org is a good place too.
If you're a go getter type, you could try some different designs and let everyone know how it goes--or if you're more cautious, you can make some drawings and post them here and get feedback from a very diverse set of bright minds. Either way, good luck.
