Lecithin is indeed a good emulsifier, available from egg whites or soy. Both egg whites and soy lecithin are available in powdered form and should be shelf-stable and usable with normal kitchen tools (scales and measuring spoons).
Another powdered option is gum arabic (also called acacia gum), which comes from acacia resin. It's used a lot in commercial food products and candies.
These are all readily available online, but you may also find them in some grocery stores (in the US, the Bob's Mill brand offers a lot of things like this) or restaurant supply stores (but the quantities might be more than you want) or you may find some gums among the spices at larger Indian markets, or certainly in a large spice market like Kalustyan's in NYC.
I know you asked for neutral, but I figured I'd also mention that garlic can be used as an emulsifier but it isn't quite as stable (it may separate some over time in the fridge) and, of course, it is NOT neutral. But the flavor profile of garlic might fit in some recipes where mustard doesn't. (There is a tasty Lebanese dip that demonstrates this well -- it is pretty much just garlic, salt, lemon and oil, and whips up into something thick and creamy.)