well, possibly. I think that I saw on another thread that you were just beginning, so it is probably a project to save for another day.
I think that you could probably use a technique called inside out turning. take this for instance (I haven't watched this person before but it has a decent picture to explain what I mean)
that will produce a 2 dimensional heart shape. add in a top and bottom after you have taken it off the lathe (like a sandwich), you have a box. with care you could glue a thick base on it and contour that.
I said that it isnt for a beginner, but there is no reason not to try it. use a cheap bit of 2x1 pine or something that doesn't matter if it goes wrong. It isnt the nicest stuff to turn but will allow you to play with the process a bit. It isnt dangerous to try (like say a big out of balance bowl for a beginner, or complex hollowing), just a little disheartening when it goes wrong, literally!
You have just over a month until valentines day!
on the same YouTube search, this came up. I dont actually like the item but...