Root applies to the ROM - you root the ROM, not the phone, so updating the ROM and retaining root is changing something without changing it. So, no, you can't. (Some updates can retain root, if you're running SuperSU and put it into survival mode before you update, but not many can.)
As far as flashing Lollipop, download a ROM (the latest one SamMobile has is 4.4.2, so
Verizon Samsung Galaxy S 4 - XDA Forums may be your best bet), then follow our
[Samsung] How to flash Stock ROM via ODIN guide. As long as you can get into download mode (Home+Volume Down+power from a power off state), you can flash a ROM. Even pressing Volume Down at the point you get may get you to the download partition. Either way is enough to flash a new ROM.
(I don't think you have an unlocked bootloader - the Verizon and AT&T bootloaders were locked from 4.3 on and there's a lot of money waiting for anyone who can come up with a way to unlock them. What youprobably have is a locked bootloader and a custom ROM.)
AFAIK, there's no rooting method for Verizon Lollipop yet that won't trip Knox, but check XDA - I haven't looked in a long time, because I'm not interested in a user interface designed to kill batteries in phones with Amoled screens.