So today we let Patty do a little romping in the living room. It was very exciting! Except she feels no fear of the lamps we have. Now, I'm not nocturnal, so I need at least one light on to be able to see her. How do I protect her from burning herself on the lamp that's on? Or, is there a best type of lamp that's safe?

If you have a place to hang tube lighting that always works well. You can also just make sure that she doesnt go near it. If you see her going by it just move her. I would suggest putting a cloth over the lamp shade but I know of someone who started a fire doing that, so I dont advise it. You may also just want to go with night lights in there.

Perhaps you can use metal window screen to make a cover for the lamp shade. This will prevent her from getting burned by the bulb but would be safer as far as fire hazzard goes.

You could also consider putting a dimmer switch on the main celing light switch. That way you don't have any bulbs where she can get at them.
But you really do need to keep her away from hot bulbs, I've heard of them getting very badly burned that way <img src="/ubbthreads/images/graemlins/worried2.gif" alt="" />.