There is a bus to Amritsar, but I don't think it runs every day. Perhaps ask for details at a travel agent.
Option 2 is very easy. Take a bus or minibus from Lahore railway station that goes towards the border, along the Grand Trunk Road (GT Road). If you catch large commuter bus service from the station, you will probably need to change at Batapur and take a minibus the rest of the way. But don't worry -- the drive of the minibus at Batapur will find you. The bus fare is very cheap -- the equivalent of 30 or 40 cents and the total journey is only 20 to 30 minutes. The minibus will drop you at the gate to the border zone, and then you walk to immigration for processing. There are some porters there who will approach you to carry your bags if you wish, and they can take your bags as far as the immigration post on the India side. There are also moneychangers on the Pakistan side who, in my experience, offer a very good exchange from PKR to INR. Don't expect to find an ATM on the Indian side.
You should go early in the day, as the border can close as early 2.30 pm (Pakistan time) and sometimes there are power outages that will delay processing. It doesn't take long to complete the processing to exit Pakistan but there is a lot of paperwork and stamping of documents on the Indian side.
You will find plenty of tuktuks and taxis waiting on the Indian side, and it takes about 40 minutes or so to get to Amritsar. If you want to wait to see the border closing ceremony on the India side, you will have a problem as you cannot take your bags into the viewing zone. I found a taxi driver and trusted him to wait with my bag and then I rode with him to Amritsar, but you may have something different in mind. You could always come back the following afternoon to watch the ceremony then -- there are plenty of people who can arrange this for you in Amritsar.