I notice that several online dictionaries do NOT include the word as used here, so looking it up would have been confusing. Use this definition: rattled
"Someone who's rattled feels confused and upset. When you're rattled, you're shaken and maybe a little fearful."
A person who's rattled might not be able to fully perform her duties or make decisions. She is distracted by the emergency.
EDIT: Addressing "a" as in "a rattled..."
We are introducing a descriptive phrase, an adjective. "A red engine" has a similar meaning; the engine is red. The "a" of "a red engine" is the indefinite article. However, with "a rattled Carrie Lam" we have the indefinite article introducing a specific person. I'm not sure that I can explain the rule for that, but it is common usage.
Using my own name, you could describe me as "a green Ed", "a rattled Ed", "a purple Ed". It's a way of introducing the adjective as it applies to the specific object or person. So, yes, "a" is providing emphasis.