Trigger a relay with a very low DC voltage
It appears you want to make some LEDs go on a signal reaches 150 &micro;V.  Let's forget about your imagined implemetation of a relay.  A low side transistor switch can do this.

However, the tricky part is how to detect this 150 &micro;V signal so that a solid on/off signal of appropriate voltage can be generated.  150 &micro;V is a very small signal, smaller than what many microphones would produce when you talk into them normally.  This won't be easy if this signal really needs to be DC coupled.

If this signal can be AC coupled, like a audio signal can, then this isn't too bad.  Such signals can be amplified, then AC coupled again to eliminate the inevitable DC offset caused by the amplification.  Otherwise 150 &micro;V will be tricky to detect.  Most comparators will have more offset than that.  For a one-off do it yourself project, you can add a trim pot to adjust the threshold by experimentation, but be aware that even modest temperature changes can require re-calibration.

To give more details on the solution, you need to provide more details on the problem.  Pop up two levels and explain what you are really trying to accomplish, but leave out any imagined solution on your part, like whether to use a relay or not.  In other words, the question should be when some well described thingy does this, a string of LEDs should light.