After a day away (finding time to do this with an infant is waaaay harder than I ever thought possible), I finally figured out a bunch of my lerping issues. Almost all of them were derived from me not understanding how lerp worked within a game loop, and while I did figure some things out - there are still many things that I have on my plate to fix.

In the gif you can see that over time, the box moves to the mouse (when I click). I have yet to figure out why it doesn't occur smoothly or consistently, but I'll just save that for another day.