Hi snowy43, I agree with Gold1locks, the best way to get rid of scale insect (the most likely cause of your sooty mould) is with fingernails and soapy water. I did this with my orange tree a few years ago, which also had mealybug - it took several weeks of regularly cleaning the leaves and removing the scale insects, but then it sorted itself out. I suspect that, when it was growing in the nursery, the tree was regularly sprayed and fertilised, and so had no natural defences to insects. It's now been growing organically for five years and has a few scale insects, but these don't ever reach pest proportions - they live in happy equilibrium with the tree.
Another thing you could do is just pop the lemon tree outside - many ladybird species love a scale insect or two