For dry dusty conditions I strongly suggest you use a dry lube. As the name suggests, dry lubes are dry after being applied to the chain. All dry lubes involve some sort of wax.
Many riders used to literally use wax to lube their chains. This provided the advantage of a very clean chain in dusty conditions, but in reality provided very poor lubrication. Some people still use wax and swear by it, but unless you are one of these people, I don't suggest it.
The modern day dry lube typically use PTFE, teflon and other agents suspended in an evaporating solvent. When the lube is applied it is wet, but after a few minutes it dries leaving a waxy protective coating on your chain.
These lubes hold up fairly well in wet conditions as well, but you may need to reapply the lube more often in these conditions.