Do you have to have bitcoin core fully downloaded (150gb+) in order to run a lightning node? Looking to setup a lightning node, but what are the EXACT requirements? Do you have to install bitcoin core and fully have the blockchain downloaded of 150gb+?
Yes. 

A lightning node needs a way to refer a copy of the blockchain that it trusts, so the node can either have it locally or might refer to one using neutrino. That would allow you to run it without an external hard drive at all. You could run a lightning node on a rpi off just an ssd card by this method.