If I can improvise on this a little.
Why do guys not lift the lid then put it back down? Well thats simple.
Now this is meant to be somewhat humerous but with some truth to it.
When you sit on the toilet well technically you dont really have to aim much cause pretty much gravity takes over but then again a man does have something to aim with but along the same line he doesnt exactly have a scope or iron site on his penis to really aim with hence why a guy doesnt always hit what they are aiming for in the beginning. As to why they leave the lid up well I bbelieve men are acustomed to kicking the lid up with there feet and just going and flushing and then turning to leave. I for one always wash my hands but personally I dont want to touch the seat regardless. Now as wrong as this is I have played tricks on my best friend before due to the whole "dont fall in" expression but I know although wrong it too has been played on me. But ladies I will assure you. Not all women are as clean as you would expect and fall into the same category as most men do as far as cleanliness and such. Ive seen womens restrooms that are just as bad if not WORSE than a mans restroom. As far as chaining a lid to the floor I think thatd be a bit much but hey to each there own. Me personally I always raise the lid but dont always put it back down cause I dont have a woman here at my home staying with me. Its all in habits ladies. A man that spends a mojority of his time alone at home is going to keep the lid up except when he uses the toilet to do "paperwork" but at the same by doing this over a long period of time he may not remember to put it back down when out in public or where ever he may be at the time. Its all in habits...they can be made but can be broken as well.
Like the saying goes: "If you sprinkle when you tinkle, please be neat and wipe the seat." and of course "No job is finished until the paperwork is done." See the lady inside of me still comes out from time to time.