Boiling Water For Pasta - With Lid On....Do I Have To Wash The Lid?
It depends. In a commercial setting - definitely not. In a private one, well, you have some leeway. However when cooking pasta you might want to add some salt and/or olive oil to the water, which might get on the lid. Also pasta might release some starch while being cooked, which might also stain the lid.

In your case I'd say it was as good as clean, however depending on how greasy your fingers are you might consider giving the top a little scrub while cooling it down with some cold water before storing it.

Also if if pot wasn't quite clean that might affect things, but essentially you've steam-cleaned the underside of the lid, and if you weren't cooking anything splashing grease around your kitchen even the top might be cleaner than when you started.

So in conclusion, it depends. Unless you can document the states of the lid and kitchen, and what criteria should be used for "clean", all any answer here can hope to achieve is give basis for opinions you and/or your roommate(s) still have to choose between =P