Do they recommend the lime to adjust the pH or to address Ca deficiencies in soil or in the plants?

4,0-4,7 sure is a bit on the low side, but microbiology can do unexpected things. According to Olivier Husson and John Kempf eh is more important than pH. Maybe listen to a talk of those together?

Ca availability is driven by microbiology. CaCO3 is quite oxidizing, so microbes don’t like it very much and it might make Fe, Mn, Cu… more unavailable. You might have to consider how to apply it, maybe big soil applications are not helpful? I’m not enough of an expert in this field to give more practical advice 🙁