Honestly, Doc, if an adult American lobster made it through an entire first year in a room-temperature aquarium and remained healthy, I would not assume its life had been drastically shortened—provided you then corrected the temperature and maintained excellent water quality.

American lobsters are naturally very long-lived; NOAA notes they can exceed 50 years of age. They also tolerate a surprisingly wide temperature range, although their preferred temperature appears to be roughly 15–20°C (59–68°F), with about 17°C/63°F being strongly preferred in one behavioral study.

So my educated guess for your lobster, assuming:

• it is already an adult,
• it survived a year around 72–75°F without obvious chronic disease,
• you now keep it around 55–65°F,
• oxygenation is excellent,
• ammonia/nitrite remain essentially zero,
• and it molts successfully,

is that it could potentially live many more years—conceivably 10, 20, or even longer. Its actual remaining lifespan would depend heavily on how old it already was when you bought it. A large grocery-store lobster could already have quite a few years behind it.

The thing that would concern me about that warm first year isn’t necessarily a simple “one warm year subtracts X years from its life” effect. I’d be thinking more about chronic metabolic demand, lower dissolved oxygen, increased pathogen activity, and stressful molts. Elevated temperatures increase metabolism and growth/molt rates, while American lobsters naturally experience much cooler conditions for substantial portions of their lives.

My gut feeling: if he’s healthy after that first warm year, you’ve probably already passed the period of greatest danger. Cooling him appropriately now could very well put him on a trajectory to be your bizarre, cantankerous, refrigerator-dwelling pet for a long time. 🦞