One way to think of the difference between an "append-only" ledger and one that isn't (e.g. LCR without checkpoints) is the difference between a strict teacher that allows no late work and a soft teacher that allows late work just the same. Half way through the semester, a clever student in the soft teacher's class who hasn't done any work can still pull off a perfect total score in the class just by cramming at the end, turning in all homework, and getting all previous zeroes turned to perfect scores. It's a function of what rule the system uses - does it allow previously confirmed ledger entries to change or not? Trustless or not. Right?
I guess it is assumed that you are watching for rule violations constantly. Once a violation is spotted, you just freeze your ledger and it remains append-only.
Checkpoints in POS (and to a lesser extent in bitcoin) add trust to the equation. You might ask if checkpoints are so great, why not have them for every single block and the obvious answer is that this means you are trusting the checkpoint producer 100%, which is against all that trustless crypto attempts to achieve.
LCR should mean that you don't need checkpoints at all; this is something which POW has over POS and all other consensus techniques which do not expend a resource to create a block.