@JohnRennie I get that part. I was just assuming that to the man in the lift the charge would be at rest at first so there must've been an electric field that moves the electron in the beginning. I just couldn't figure out the source of that electric field because the wire is neutral for both the observers

Ah, ISWYM. No Lorentz force because the charge isn't moving.

@JohnRennie This example doesn't confuse me as much. I understand that magnetic and electric field are expressions of the same phenomena and treating them separately only works when confined to a single frame

I'll have a think about it.

Sure sir :)