If morgan pendleton is in the steam room, this is easy, just go down there, as you reach the basement, you'll see two doors that require the master key. You want to go through the red gated door, without the master key. The fast way is to go through the vent that is just up and to the right of the gated door. Grab the steam valve and put it on the wheel and use it.
If on the other hand morgan pendleton is NOT in the steam room, this is a little harder, but not by much. he'll probably be in the smoking (or Ivory) room. First grab the master key from the madam of the house, (you'll want to get this before you grab morgan as he's on the way to the steam room and you'll probably alert the guards when you grab him.) The Madam is in her office, on the right side if you face the Golden cat from the outside, or talking to the guard if this is the first time in.
After you get the key if you're on easy mode, just sprint to Morgan pendleton and knock him out. (Stop time, just use a dart, what ever you want to do. DO NOT KILL HIM)
Grab his body and run down to the steam room (there's signs over the place, it's in the basement off of the main areas of the golden cat) Just run and use stop/slow time if you feel like it. You're going to want to open the vault looking door, throw Morgan Pendleton in. It's IMPORTANT that you don't throw him in the water, put him down beside the water.
Then run back to the red gate and turn the steam valve and it'll kill him. You ONLY need to kill morgan pendleton with the steam. Even if you have to knock him out and drag him down there, it's fine, as long as he dies when you turn the valve.