Well, that is a tough question, because there is a great degree of discussion around it.

Regarding LB, even today, some experiences made to reproduce range and armour-piercing power, are quite unconclusive.
I had a talk in another thread with dunnichen that discusses some of these new experiences:

Archers Underpowered in MTW

Relating to Mangonels and Trebuchets, I believe you're right. I do not have historical information to corroborate but, they shouldn't have a similar range to catapults.
The range should be longer, because these engines were much more powerfull and had a longer projection arm than catapults.

Since in MTW Catapult Range = Trebuchet Range = Mangonel Range = 12000 units and 5000 units = 100m, we can see that their range is effectivelly:

12000 units = 240 meters

Quite short, don't you think?

I think for trebuchets and mangonels the distance should be between 15000 units = 300 meters and 20000 = 400 meters.

And this only because the maps aren't that big...

Of course, someone else might disagree.