The generic name for it other than clay lube is just 'quick detailer'. Not a high end one with all levels of slickness but a cheapo would work.
as for homebrew-it's simple. Soapy water, just like what you wash your car with will work fine as a clay lube. Personally, I like ONR QD as aclay lube because I go through roughly 24oz of 'clay lube' for the average vehicle and ONR QD for the price can't be beat.