That is one tiny bonsai tree. It's fungus/mildew whatever you want to call it. In Florida they have leaves like that all the time, pretty harmless. You can spray it with neem oil which works pretty well if it sits out in the rain or gets sprayed with a hose. The oil will stay on the leaves for a while and eventually wash off with enough waterings. But if you never water the leaves with a strong jet or rain, then I would stick with copper.
When I sprayed my lemon with neem oil it didn't damage it and it killed some insects I was having problems with and kills fungus. I don't know how citrus reacts to copper. On my grapes the neem oil does more damage to the leaves than copper, but usually pretty safe.