You may be able to use the ultrasonic sensor and an Arduino to detect if there is some one on the stair so no timers are needed, just keep the LEDs on while the stair is occupied. It depends on the length of the stair and the sensor used. My vote is to go Arduino over a 555. Getting an Arduino can be very cheap and allows you to easily change things, unlike a 555 that is quite fixed in its function. Like for instance, add an LDR so the LEDs do not come on when it is already light. You could do that on a 555 by driving the enable too, but it is just an example. With an Arduino, and an ultrasonic sensor you could have just the LEDs near where the person is walking come on, moving up or down the stairs with them. Then would be pretty impressive.

 

I've found the ultrasonic sensors to be unreliable for anything that isn't flat and large. In particular they are bad for detecting people. Curved surfaces (your body) reflect sound away from the receiver, and soft clothing absorbs sound decreasing range. It all adds up to inconsistent detection. I'm referring to the cheap HC-SR04 type devices, maybe better hardware will overcome these issues.

Initial testing shows these two sensors work better, the first one might be a better fit for your project, especially if you stay all analog (no arduino):

IR, 1.5m range, analog voltage output: https://www.pololu.com/product/2474
Laser, 2m range, I2C interface: https://www.pololu.com/product/2490

 

Although in thinking about using the 555, i would need 2 ouputs for the ultrasonuc triggers, 2 inouts for the ultrasonic echo pins, anc an outputfor the led's...I fon't think I can do all of that with a 555..