Is the person trapped in
The Statue of Liberty?
.
- "fiiiiine lady": Lady Liberty
- "quite free": a symbol of freedom
- "gagged and bound": The poem at the base of the statue notes its "silent lips"
- "inside a fire": Perhaps trapped inside the torch? The poem at the base of the statue even calls it the "imprisoned lightning"
- "there's water nearby": the statue is on an island
.
Another fun fact: There is a DC character named Lady Liberty
edit: about who the person could be:
The Statue of Liberty's poem was written by Emma Lazarus. This reminds me of the Lazarus Pit, so maybe the Joker has kidnapped Talia al Ghul? The Lazarus Pit is used for resurrection as well, like the resurrection symbol found in the LSB decoder.