the problem with lubricating this type of chain is to get the lubricant where it needs to function - the internal parts of the chain (pins, rollers etc). this calls for a oil that has good creeping and penetrating properties to get it where you need it and also, because most of the relative movements that need lubrication only make small movements, for good adherence and antiwear properties. you may also want to have good anticorrosion properties to protect the exposed outside components of the chain. finally, because excess lubricant may well drip off into the environment a biodegradable fluid is to be preferred.
most modern chain lubricants nowadays are ester based and are available in a range of viscosities, some contain a diluent that helps in getting it where you want it and then evaporates.
there are various lubricant suppliers that offer a range of specialised chain oils and you would be best served to contact them for advice on this specific application.
another important aspect to consider is the way the lubricant is applied. incidentally it can be applied by a brush, but systems that supply a small amount of lubricant by spraying or brushing usually can prolong chain life considerably.