So, I'll answer myself, as I now know that the Lavor surface cleaner is compatible with the Lavor HDR 140. I just took the risk and bought both, and there you go, it fits.
I think it's a shame that "asking the dealer professionally" leads to wrong information.
The Lavor surface cleaner works, but it is not enough to clean very dirty floors.

According to our enquiry with the third-party supplier, the two items are not compatible with each other.