ALDEVAUX

The spots shown on your pics definitely look like leaf spot of elms caused by Stegophora ulmea.
It is not true that these spots do not infect old leaves although the younger leaves are definitely much more susceptible. There are also different strains of the pathogen, the inported one being most aggressive on young elm shoots. Some strains attack mostly older leaves.
The normal control for this disease is to apply fungicidal sprays early in spring, and before rainy periods because the fungicides can only protect healthy tissue and do not eradicate existing infections.
As in your case, when infections have occured before fungicidal applications, you should not expect infected leaves with visible spots to become normal. Many of the leaves which do not show visible spots could also be already infected because they are not visible during early stages of infection and they will eventually show up even after fungicides have been applied because the fungus is inside the leaf where the fungicide does not go.
The only thing that the fungicide can do is to protect non infected leaves to be infected by the fungus as it kills the spores before they can germinate to enter inside the leaves. In other words, the fungicide is effective only as a preventive measure.
The best way to protect non-infected leaves is to to use a sprayer that will deliver a very fine mist that will cover completely both sides of the leaves especially the undersurface where most infections take place. This is the kind of complete coverage you will observe in orchards when they are sprayed to protect the trees from fungal infections. Spraying with a watering can is innefective and a waste of the fungicide.
Furthermore, the sprays should be renewed every 15 days, or earlier when the leaves are wet, until all the new leaves do not show anymore infections.