it seems like the Rome to Catania flight was a "separate" ticket. If so, you are SOL. Fair or not, the airline has a contract to get you from point A to B. So TAP won't be liable to reimburse you for your onward booking.
If in fact you had one single ticket (multiple airlines is fine) Miami-Lisbon-Rome-Catania, the airline is liable to get you to Catania (even with flight delays).
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