After you take Eileen to the elevator, select bottom floor from the panel. Go out the door here, and look for the Holy Candle in a corner. Take the Candle if you'd like, then get Eileen to follow you around to here. Push her into that corner, and make a fast break for the Elevator farthest away from this corner. Enter it as fast as you can. If Henry appears alone in the elevator, you've done it. If not, go outside and try the whole process over again from pushing her into the corner until he does appear in there alone.
When he finally shows up in the elevator alone, go down the ladder in here.On this screen, continue forward along the linear path until you trigger the two Walter cutscene. Then continue along to the next screen -- you should notice Eileen on the other side of the fence along the way. After this, go back to the previous screen. You should wait where you enter, and you'll eventually see Eileen running straight at you on the right side of the fence. Now you can continue along to the Bar where you can enter the door code, since you don't have to escort Eileen the long way.