It’s been a very long time since I read the book, but as far as I remember in the biography of the L rebbe, “Larger than Life” by Shaul Shimon Deutsch, it says explicitly that the L rebbe’s parents – I think it was davka his mother – knowing that Chaya Mushka could not bear children, only agreed to the shidduch on condition that their son would take over after the Rayatz.
I also once heard from a reiliable (but not impeccable) source, that the reason the L rebbe and CM left for Berlin so soon after their marriage was to seek treatment for her infertility.
How unfortunate that he did not have any children, as had he had a son it is very likely that we would not have the Mashiach meshigass that we have now.