This situation could constitute a violation of your lease, as well as the state's warranty of habitability and the city's noise code. First, look up your building's certificate of occupancy... If a gym is permitted in the building, you could still argue that the landlord is violating the city's noise code or your lease.
The noise code prohibits excessive sounds that disturb the peace, comfort or repose of a reasonable person. Decibel measurements are included in the code, but they're not inclusive of all instances of unreasonable noise.
Before you call a lawyer or a city noise inspector, tell the landlord that they must visit your apartment to witness the noise... you should be able to make a case that the building needs to effectively soundproof the gym.
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