What did they tell you that you needed to do to the railing to meet code? Not all jurisdictions have the same code.

No more than 4” spacing on anything above 30”.

Why is it needed? Is it a case of a buyer having a VA or FHA?

Add spindles to it and make sure it's 36" from the deck to top of the railing.

VA

What about hog wire? Could that be cheaper todo?

You really need to check with where you live what is allowed. Hog Wire with the small spacing added on the outside with some boards holding in place would work where I live and be fairly inexpensive, but you really need to check what is allowed in your area. Sometimes something that can be easily climbed isn't allowed such as horizontal anything so it really depends.

Or maybe some kind of lattice?

I wouldn't use the lattice, most lattices on the market are stapled together and pretty flimsy, unless you can find a structuraly sound lattice but it's not going to be cheap.

pickets, the spaces between the vertical lumber are too large/open. Home Depot/Lowe's. Anyone with a level and a drill with a box of fasteners/screws can do it.

Pickets?

Just add more horizontal 1x4s between the existing.

Debbie Christin, maybe where you are they call them spindles.

Pickets are the spindles of the fence world. :) And fencing materials are probably what you need.

I'd do like Seabornman suggests and put in more horizontals, though. The horizontal lines of the railing are too perfect with the house to mess up with more verticals. Style matters!