It works fine without cellular. In the hands of someone who can install Linux, it shouldn’t take more than an hour (if you have a not-dialup internet connection).

First, apt install adb heimdall-flash. These are the basic tools for interacting with Samsung phones and Android devices in general from a Linux machine.

From there, follow the instructions I linked below, which basically amounts to getting root and unlocking the boot loader using Heimdall, then flashing TWRP, which is a recovery program, then flashing LineageOS from within TWRP. It’s not hard, but be sure to follow the right set of instructions, because the files for the Verizon, AT&T, and Sprint phones are not compatible.

Assuming you have the Verizon model: https://wiki.lineageos.org/devices/jfltevzw/install

Thank you for these instructions! I am going to try later this afternoon after some family stuff.

There is an active community of developers, who are keeping the Galaxy S4 alive by creating optimised versions of LineageOS. It might be easier to consult the guides and resources at XDA. If you feel it is a task you want to undertake - assuming the bootloader is not locked, decide which version you want to install based on the model you own i.e. i9505 or another variant and once you flash custom recovery (TWRP), it a fairly easy process.

You should expect to face some issues initially and will have to go through the forums/comments to trouble-shoot broken features etc., especially if you are picking the latest ROM.

https://forum.xda-developers.com/galaxy-s4