Can I make this assumption about the utility function?
No.

In general, based on the information you have, there are no results you can infer for the partial derivatives $U_{cl}$ / $U_{lc}$. In this context they could be anything.

As to what you are allowed to assume is a different story. You can assume anything in general, of course. Nevertheless, there is no way to check if your assumptions would be correct in this case.