Can anyone tell me the disease and/or solution?

My lemon tree's branches are all quite black and most branches are
covered in what look like insect eggs on them (colour and size of sesame
seeds). The underside of the leaves are mostly okay but have some of the
same eggs.

Are these indeed eggs and is the black colour some fungus that is
related? Will malathion or white oil fix it?

TIA, etc.