Plumbing: Drain Pump For Laundry?

That'd be four pipes up in your lowered ceiling: hot water, cold water, drain, and pump vent. You'd need room next to your washer for the pump itself. The pump'll require an indirect connection to the washer, i.e. washer pumps to a sink or stand pipe which drains into the pump.

All that's very elaborate and prone to failure. For instance, when lint from the washer clogs the pump and causes it to shut off, while the washer continues pumping, the water's going down on your neighbors.

I'd make sure your condo/co-op permits wet-over-dry before getting into the mechanics of it.

how are your floors?
I have run up to 20 ft as long as you have a gradient of 1/2 inch per 4-5 ft length you want to go.
It didn't bother me that I went into the rubble/sub floor 6 inches as I was replacing the floor above in that area anyway. Hence I had to go down about 6 inches, 2.5 inch for the width of the pipe plus another few inches so there was a gradient for the water to flow.
Additionally I always put down a pan with an automatic shut off
Good luck

What would a project like this cost? Considering something similar