The LCR insures no double-spend exist.
Once quantum computers hit the market everyone will be able to rewrite complete Bitcoin blockchain from the genesis. So I would add something to emphasize temporal nature of your statement.
Quantum computing does not significantly speed up PoW because it is hash based (thus Shor's algorithm doesn't apply). So you must mean that ECDSA signatures could be cracked and double-spent?
But same as for a 51% attack that is not a threat vector because no one will honor that. Politically it is an impossible attack.
And still there is no way to recompute all that PoW and arrive with a longer chain, so no attack exists.
Besides in my current design I use Winternitz signatures that are not subject to Shor's algorithm.