A few technical questions re: transport and passport control

First I would not buy tickets till I am in the train station. You just don't know what can happen with your airline and getting to the station. Get to the station and buy your tickets. If early you can catch a light dinner in the station or near by.

The metro in Lisbon can get you from the Airport to the the Lisboa Oriente train station in just six minutes. Your best bet, though, is the 60-minute flight on TAP Air Portugal departing Lisbon at 8:05pm on October 11. Tickets currently are being sold for $30 through Skyscanner. There is a similarly-priced flight at 5:55 pm which could work if you only have carry-on luggage.

www.Skyscanner.com

Thank you. Both good suggestions that I will consider. Taking a flight would certainly ease connections much easier, but we'll both have checked and carry-on luggage, which increases the cost considerably. Buying a train ticket in advance has a considerable discount, hence my interest in knowing what adjustments can be made if unforeseen events result in missing a connection.
Perhaps it's not doable, but I'd like to explore all the options.

TAP Portugal Airline will add a 55- pound checked bag for $37 more.

A “Normal Fare” train ticket for $38 from Lisboa Oriente to Porto is fully refundable up to 15 minutes before the train’s departure time. There are trains taking 3 hours departing from Lisboa Oriente station to Porto at 6:09 pm, 7:09 pm, 7:39 pm, 8:09 pm, and 9:09 pm. The fares run up to $40.

The biggest issue is the weather in Terceira on the day you fly out. In October, and really any time of the year, the weather in the Azores (actually every island could have different weather) is probably what is normal, but not guaranteed. The plane flying to Terceira could easily be delayed.

Trying to purchase a train ticket this far in advance is not what I would recommend. Unless you are flying TO Lisbon on a ticket with a connection TO Porto on the same airline, you are on your own if something goes wrong.

With a ticket on a connecting flight, and on the same airline, if something goes wrong, the airline will take care of your logistics to get you to Porto ASAP, which means it could be the next day. Your hotel, taxi, and food will all be free with vouchers for an unplanned overnight in Lisbon.

Based on what seems like you already have a flight booked to Lisbon and not one continuing to Porto, buy your train ticket to Porto only when you are physically at the Oriente train station in Lisbon.

Terceira to Lisbon is a domestic flight, no immigration delays, pick up your luggage and go.

For the Metro you'll have to buy the Navegante Ocasional card to load the fare to Oriente - I saw plenty of individuals trying to "help" tourists buying the fares from the machines ( only one was actually from the Metro, I guess the rest expect a tip).
https://www.metrolisboa.pt/en/buy/

The train tickets can be purchased a maximum of 60 days before departure, usually at a discounted price.
The AP train is the fastest ( first class the most comfortable - wider seats).
If you miss your train, go to the ticket booth at Oriente, explain the reason for the delay, they usually replace the tickets ( it happened to us and they gave us tickets for the next available train).
Oriente train station has 4 levels, Metro is on the lowest, trains on the top, ticket booths are one level below the trains.
Ask which platform is the AP train going North.
Other local trains use the same platforms, ensure you're boarding the correct train.
https://www.cp.pt/passageiros/en

There are some good suggestions here. But in my opinion you are approaching this from the wrong angle. If you want to travel from Terceria to Porto, I don't think flying to Lisbon is the best option. Azores airlines has a daily direct flight from Terceria to Porto, that would be my choice. https://www.azoresairlines.pt/en

When we booked our flights with Azores Airlines their regulations did not permit both an open jaw (arrive Porto, depart Lisbon) and courtesy stops in the Azores coming and going. We opted for the Azores stops. We didn't consider traveling to Porto from our flight until a few weeks later, hence the conundrum.

With all the valuable insights and information you've provided, especially the weather issue, obligata Carl, I'm starting to rethink this. Perhaps we'll be better off staying near the Lisbon airport on the 11th and taking a flight or train to Porto on the 12th. Will discuss with my sister.

Many thanks to all of you for taking the time to thoughtfully respond! You've opened my eyes and your suggestions will result in an easier and more enjoyable experience.

Please know that at the top of this Portugal forum is an Azores post written by the webmaster. In it you will find a link to my digital Azores guide on Amazon.

The first 52 pages of my guide are totally free to read. The logistical information within those free pages will definitely help for your Azores trip, especially while in Terceira. There is NO OBLIGATION to purchase my entire guidebook!

I am always a private message away if you have specific Terceira/Azores questions.