What does the Lewis structure of ClF4- look like?

How about an attempt or a guess and then we'll guide you from there?

Requires you to understand how to calculate formal charges.

So draw out a molecule (hint... when in doubt where to start try a symmetrical molecule... doesn't always work, but a good place to begin) with bonding and nonbonding electrons and then calc formal charges.

Here's a HUGE hint... chlorine has d orbitals which allow it to exceed the octet rule while fluorine does not. In other words, each fluorine will never have more than 8 valence electrons, but the chlorine can have more electrons... this is impt when calculating formal charges and adding enough electrons to match the molecular charge.

There are 36 ve in the structure. If fluorine can never have more than 8 ve, then I think that there would be two lone pairs of electrons around chlorine in addition to its single bonds to the other four fluorines. Is that right? That would mean that chlorine has the -1 formal charge. But fluorine is more electronegative than chlrorine. Would this just be an exception?

Yeah, even though you try to put charges on the more electroneg element when forming a lewis structure, there really is no choice but to put it on the chlorine, as it is the only atom to have "room" for the extra electrons needed to get the charge down to 1-.

Sorry took so long to get back to you.