Is it lashon hara to tell someone that someone broke an engagement?
This is not in principle lashon hara. Breaking an engagement does not necessarily reflect badly on any one of the parties, and although unfortunate, it sometimes happens, just like couples sometimes get divorced.
However, it is forbidden to tell this over if said in a derogatory or accusatory way, implying that one of the parties was at fault and meaning to denigrate.
Note that although the matter of a broken engagement is generally known, it remains forbidden to spread the word if the intention is to denigrate.