LMR-240 is Times Microwave and has the standard PE jacket. Andrew Commscope has a version with a PVC jacket that has more flexibility. we find with most applications it is not the relatively thin cooper center that is not flexible its the tough outer jacket.
If you are running it outdoors or expect abrasion use the PE jacket version, if you are using it for jumpers and want extra flexibility use the Andrew CNT-240.
In reality Times and Commscope both make many versions of jackets for both 400 and 240
Standard with a PE jacket
FR with more flex and a fire rating
PVC that is real flexible
UltraFlex which is rubberized with a braided center
also a few other types of Plenum jackets
As always - watch for the bait and switch.