Is it possible to wire an accelerometer straight to lights?
Unless your accelerometer has an output pin that it lights up when triggered, no, you cannot directly control the led without some sort of middleman microcontroller.

If it does, then you can use a comparator as mentioned in the comments, and a mosfet or transistor as a switch.

Considering how cheap and easy it is to get a microcontroller to do this, it would be quicker to use one then shifting through datasheets to find an accelerometer that does what you want directly.