White spots on lemon tree
Thank you for your question about your mother's lemon tree. I can't see the spots very well, but think it is probably a lichen, a combination fungus/alga symbiotic that lives on tree trunks and leaves, especially when in the shade. The other possibility would be a fungal infection, Phytopthera, but you probably would be seeing oozing and cracking of the bark. I've attached a photo of a citrus tree with this.
More likely is the lichen, and you'll find pictures and a discussion of the comparisons between the two here Lichens cause no harm to the host plant, and are not parasitic (using anything of the plant's except space). There are other problems with citrus trees listed in this Extension article that you might want to peruse. I would take a 'wait and see' approach or snap some closer-up photos and send. Good luck!