Well. I've got a lemon, orange, kumquat and lime-quat growing outside
here and periodically they get scale infestation that can be followed
by sooty mould. This spreads and is nourished by the sugar-rich
exudate produced by scale insects and mealy bugs. I'll concur with
the remedies already suggested, although in the absence of a natural
predator to deal with the mealy bug, you may have to resort to a
systemic insecticidal spray if the lemon is a large plant/tree.

You will need to check your local garden centres for suitable products
since they are unlikely to be the same as those available in the UK.
Since our climate appears to be getting increasingly milder and now
easily capable of sustaining lemons out of doors in the south at
least, your question is relevant and the problems you've experienced
also occur with UK plants grown under glass anywhere.