$another_variable is a lexical variable...
Strictly speaking, $another_variable (as the OP has it) isn't a lexical variable. my declares a lexical variable — no my, no lexical variable... (maybe you meant to say it should be a lexical variable?).
In the OP's case, both variables are package variables, it's just that strictures do not complain if you use the fully-qualified form, even if the variable is otherwise undeclared (the idea being that you know what you're doing if you spell it this way).
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