This is a fungus/virus/bacteria but it is growing inside the leaf so neem oil or baking soda will not control it.
The most likely cause is overwatering. When the roots cannot get enough oxygen because the spaces in the soil are filled with water infections like the ones seen in your picture move into the weakened plant.
- reduce watering
- improve drainage
- improve light levels
Most plants can outgrow the infection if the cause is removed.
Black spots on leaves are most often a fungal infection. You can either remove the leaf, ideally without waving it around in the air thus circulating the spores, or apply something like Neem Oil which is an anti-fungal solution. You may wish to dilute it (1% product to 99% water) to start with, or apply sparingly.
Or you can try a more traditional treatment by spraying with a mild solution of bicarbonate of soda (baking soda), using ½ teaspoon per gallon (2.5 mL. per 4 L.) of water.