Thought experiment, a really long lever

[Aerozord]

so last night I was thinking of the quote "give me a long enough lever and I will move the world" and went, what if you did have a really long lever.

This led me to the following thought experiment

You have a lever thats, lets say 100 million lightyears long, and made of a perfect solid that doesn't bend or brake. Fulcrum at one end and force applied directly above it. You have nigh-limitless force to apply to it.

Now what would happen? Because of the length even an incredibly minute amount of acceleration would cause the other end to break the lightspeed barrier. Made me wonder if there is a minimum amount of force required to break inertia, and if so would that make the lever immovable in this manner do to limit on acceleration at the other end?

Other is what kind of odd effect that would have on the center of gravity and equation for a lever, since the kinetic energy would increase exponentially and center of gravity would change due to the changes in mass. In fact would it be an instantaneous or a progressive change?