Is it possible to have "la que"?

Hola Hans,

In this case you need "lo que" because it is referring to "The thing that", as a neutral thing/idea. So, we could say:

"The thing I hate about you is your coldness." or "What I hate about you is your coldness." 

There is a very similar example in the lesson:

Lo que admiro de ellos es su tenacidad.
What I admire about them is their tenacity.
The thing that I admire about them is their tenacity.

I hope this helps.

Inma