I am a not very bright undergrad student working with LAMMPS, and I was having trouble understanding why the hydrogen epsilon is zero. The error: ERROR: Water H epsilon must be 0.0 for pair style lj/cut/tip4p/long. It is my understanding that epsilon represents the well depth, why is this zero for hydrogen

That is how the TIP4P water models are defined: 8.4.3. TIP4P water model — LAMMPS documentation

Thank you. Do they talk about why they choose to do that in the link you sent?

Why don’t you just read the page?