Low frequencies are mostly transferred through the walls and floors themselves - so you would need to separate the walls, floor and ceiling in your living space from those of the elevator shaft. This would be very difficult to do.
Sound can be reduced in the floor because carpet & pad are soft materials. The walls and ceiling would be difficult to soften because wallboard is rigid. If you line the room with matresses, you will reduce much of the sound, plus have a beautiful new firehazard decor.
Sound tiles will absorb some, but not much of the low frequency sound - they are meant for higher frequencies.
I can't give you mcuh help on how to solve the problem - but hopefully what I've given you will keep you from spending money on something that won't deliver the results you're expecting. Or maybe the matress idea will spark some other brainstorm - some other material you could use.
Just to recap - you need to install something soft & flexible, as opposed to something rigid.