You need the /e modifier to cause the right side interpolation of the variable: 
s/\b($old)\b/(lcfirst($1) eq $1) ? lcfirst($new) : ucfirst($new)/gei;

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Consult perlman:perlre for more details.

Update:
I think I may have mis-interpreted the question. It has been since corrected, and the difference turned out to be slight.

In reply to Re: Case-preserving substitutions by jryan
in thread Case-preserving substitutions by wasii

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