Sprinkle the gelatin over the lemon juice in a microwave-safe container, ideally the container you're going to use for the dressing. Let the gelatin soften briefly, then whisk in the egg with a fork and microwave on high for about 35 seconds. You want to get the temp to 160 degrees to kill any salmonella in the egg. (I use an instant-read thermometer to make sure it has gotten hot enough, although in reality it's very rare to get sick from a raw egg. It's more for my own peace of mind than out of any real danger that I go through this procedure, but I'd need to heat the liquid anyway to dissolve the gelatin.) If you find that the temp isn't up to 160 and you want to re-whisk, use a clean fork. You don't want your fork or whisk to have uncooked egg on it. Once you've done this a few times you'll know how much time you need for your particular microwave.
After you've blended the egg/lemon juice/gelatin mixture add in the vinegar and other ingredients minus the oil. Then slowly pour in the olive oil and blend until completely emulsified; you can tell this has happened when the color becomes lighter and the dressing looks creamy. If you use a stick blender for the mixing you can just do this whole recipe in the container, but if you're using a blender or food processor you'll have to transfer the mixture to that and do the blending and then pour it into your storage container.