Arrival in Lisbon by plane at 6 am

Check with your hotel to see if you can leave your luggage there while you sight see. There might be a chance that your room might be empty and they can check you in at that time. You probably won't be there before 8 AM after you land, unboard, clear customs, find your way to the hotel. You have nothing to loose. Have fun

The hotel may let you leave the bag while you go sightseeing.

Marcia, You will love Lisbon. It is safe and we used uber a lot there or you can if you want to.

First, it has been very rarely for us not to be able to check-in early at our hotels. If the room was not used the night before, then the you can check-in. We have always been able to leave our luggage even if the room is not available. So go to your hotel, leave luggage if room not available, go find breakfast somewhere. Then do a walk around the hotel for orientation. Find a TI, and see what is going on in Lisbon that week. Maybe schedule a walking tour later that day. Try to id a lunch place. Don't get on any hop on/off buses. Save that for the next day. Take a nap, max two hours, around 2 to 3 pm.

You will be surprise how quickly the days go.

We had a very long wait at immigration last summer-ours was 4 hours. Hoping yours is better but be prepared. Once you are through, cabs and Uber are readily available. Drop your luggage, hopefully you can get a room early, go here for lunch https://www.timeoutmarket.com/lisboa/en/.

Stay out in the (hopefully) sunshine to help with jet lag. Walking around the area of your hotel is a good idea. Go down by the river and walk - just generally get the feel of the city.
A previous poster mentioned the TimeOut Market. While it's something you will want to see - don't go at regular mealtimes as it’s so crowded. Arrive before 12:30 or wait until mid afternoon.

My wife and I took that flight three weeks ago although we were connecting to Milan. Good flight, will be on-time unless there's an ATC delay in Boston because it's the same equipment that does the LIS-BOS flight earlier in the day. Equipment is an A330, with more leg room than an US A330 would have. Passport control was a pain, it took us over an hour to get through it. Don't dawdle getting off the plane. I agree with what everyone else suggests. You'll be surprised how quickly you will adjust to the jet lag. Even though it will be 1 AM back home, the fact that it's daylight in Lisbon affects your internal clock. On our trips, by the next morning we've adjusted to the time change.

Drop off your luggage and treat the first day as a "light day" just to tool around and get your bearings with no pre-arrangements or scheduled activities (save those for the next days after you've had some sleep). I like taking long walks interspersed with coffee and food breaks, and just using the time to get acquainted with a new city. It will feel great to finally get out of the plane and stretch your legs (and to get some sun, which will help you stay awake along with caffeine, of course).

Thanks to everyone for the comments and suggestions!