Battler could not repair the chain lock from the outside because he didn't have time. Erika/"Erika" was not in the bathroom for long enough to engage in any complicated maneuvers.
Metaphorically, the reason none of his methods worked within the Logic Error itself is because the Logic Error solution was not based on the actions of one person from the start. Battler in fact could not escape alone; he did escape, and he did so with Kanon's help.
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