No question, that the LH/LX staff managed your case in a wrong way. Very likely that it was the staff at LHR, but it could have been the LHR staff as well. Maybe both made mistakes.

LH/LX have to pay compensation for that plus your expenses for the night. They will lose money on your booking and you can be sure, that they are at least concerned about that.

I still don‘t understand, why you let the LHR staff rebook you on such a late flight. And I don‘t understand, why you return to them again and again, if you consider them being monkeys. If someone is not helpful (and rebooking on LH915) wasn’t, I try to get the help from someone else. Even at the same hotline number it can make sense to hang up at call again, if the agent is not helpful.

It always makes sense to ask for a specific flight to get rebooked on. You don‘t have to do that, it‘s just helpful to make the best our of the incident.

BTW: On most of my irregs I got rebooked in a smart way without doing anything. Of course they try harder to make me satisfied, but even without HON/SEN there is a process, where people get rebooked. That process stopps, if you get rebooked already.

Finally: From my point of view bad ground staff is better than no ground staff.