Hi. I'm trying to find a function or way to compare two cells and then
label them according to if one cell is lesser, greater, or the same as
the other.

I have a large data sheet where I want to compare many pairs of cells
and then have them labeled in this way. For example for each pair
where the second cell value is larger than the first it would put
greater, where the first is larger it would be lesser, etc.

Here's one way.

Suppose column A holds the first of each pair and column B holds the
second.

In C1, put
=IF(B1A1,"greater",IF(B1<A1,"lesser","equal"))
and extend downward. (Note that I included the case of equality.)

Customize to your needs.