Thanks for the question, this is an interesting topic. It seems that the main requirement is for Phosphorus - not Calcium.
Truffle soils have a high pH and are dominated by Calcium, but this also locks up Phosphorus in a form that plants cannot access on their own. However, research has shown that the fungi do utilize Apatite (basically Calcium Phosphate) and also (within the Brűlé) they dissolve Limestone and re-precipitate it as very fine "Active" Carbonate. It seems that the Lime is actually there to drive this process within the Brűlé and keep the Phosphorus in a form that the Fungus can use - and then supply to the tree.
For this reason, I have been suggesting the application of Rock Phosphate (Apatite) rather than Superphosphate or other soluble P. This is also important because high available (soluble) P is associated with high levels of Hebeloma inffection. This means that the soil test (ideally) should show a high Total P, but low available P.
A secondary requirement may be for Magnesium as Black Truffle production is known to respond to the application of Dolomite. However, this could also be related to the effect Magnesium has on soil hardness. This will restrict root growth and (potentially) stress plants, but fungi will be less affected - making the symbiosis more important.
I hope this answers your question, but if I can help further please email me: dirtdoctor@the-living-soil.com