I used Neem on my outdoor planted lemon tree, it worked. I am not an expert, but a homeowner.

Neem oil will certainly not hurt the plant but it is not the most effective treatment for scale. Many types of scale have a hard or solid exterior 'shell' that limits the effectiveness of most contact pesticides. Any treatments need to be applied to the nymph or larval stages before they develop that hard exterior. A systemic is the most effective treatment but not considered organic. Horticultural oil works also but again, like neem oil, you need to be very conscious of the timing.

I agree with GG; I have found the light horticultural oils to be more effective than neem oil. Also less smelly. By some standards horticultural oils are organic; I don’t really mind one way or the other in this case, as it will stay on the outside of the fruit and washes off easily in the kitchen.

With oils one is trying to smother the scale. Even after killing an adult scale their eggs can hatch from under its dead body. These hatches can go on for some time. One must repeat at an interval of about 7 to 14 days for some time; perhaps months. Temperature will affect the time it takes for hatching, and the time it takes for new scale to reach breeding age. At some future time one can clean all the dead scale and sooty mold off the leaves and stems with insecticidal soap (and some elbow grease).

Best of luck.

Use Horticultural oil spray after you physically remove as many of the scale as you can. Coat the leaves, undersides and stems.