The White Castle · Board game rules
Can a Lantern action bonus be skipped?
Quick answer
The rulebook doesn't explicitly state that Lantern Rewards can be skipped — you receive all visible icon benefits, though you may choose the order in which to apply them.
Details
When a Lantern icon is activated, "you receive the benefits of all the icons that are visible in the Lantern Area of your personal Domain, in the order you choose" [p.12 — Lantern Rewards]. This phrasing indicates the rewards are mandatory to receive, but the sequence in which you apply them is up to you.
The only flexibility mentioned is about order, not about opting out of any individual benefit. There's no rule stating you may decline or skip a specific Lantern reward.
Watch out: Since Resources are capped at 7 per track, if a Lantern Reward would push a Resource above that limit, the excess is simply lost rather than being something you can choose to skip in advance [p.5 — Gaining and Paying Resources].