Yes lui refers to the mayor.
Your sentence is understandable but would likely be stigmatized because it looks like you translate "Camille’s chest" by "la poitrine à Camille" while "la poitrine de Camille" is expected.
You can then say:
L’écharpe de maire barrait la poitrine de Camille.
or just reword the original sentence that way:
L’écharpe de maire barrait sa poitrine.
See also:
Limits on the Use of the Indirect Object Pronoun to Indicate Possession
Possessive adjective before a body part
French possessive adjectives vs reflexive pronouns (when to use and how)
Usually, lui replace a "complément d’objet indirect" so yes it is replacing maire. It could be also formulated as L’écharpe de maire barrait sa poitrine without going through ‘lui’, but that would be vague without any other explanation about the person whom the écharpe is barring the chest.
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