In Belgium we can find dry white mulberries in Chinese shops. I find them basically tasteless. The dark ones taste much better, but can't be found. I bought a small pack on amazon, and tried them in a small batch of mead. Tasty, very sweet, but (because they are dry?) quite raisin-like.
So I don't know what fresh mulberries taste like. if I could lay my hands on some fresh dark mulberries I would certainly use them in mead. And then decide whether they fit in lambic.
These are the "proven" fruits/additions that I know of to use in a lambic: apricot, raspberry, sour cherry, blueberry, some types of grape, plum, strawberry (difficult because not much taste), redcurrant, elderflower. Probably also blackberry and gooseberry, though I haven't tasted those.