Mobility issues and lines

There are some ‘hidden’ elevators both from Baixa to Chiado, and Baixa a good way up to Alfama. Unfortunately, trying to explain here would be quite difficult.

As I have aged and don’t want to do so many hills, I take Uber of Bolt around Lisbon more frequently. They are quite reasonable here and save my knees.
The other idea, if you want to walk around the city, would be to hire a private guide right after you arrive. You could likely do a half day tour that might not be cost prohibitive. You could let that guide know of your limitations and request they show you some of the shortcuts, as well as, some of the city.

And, remember, there are many, many cafes where you can stop for a coffee, water, etc. and rest when needed.

I agree with Kathryn that the easiest way to avoid the hills is to take either Uber or Bolt, they are relatively cost effective. My favorite short-cut from Baixa to Chiado is to take the escalators up from Baixa to Chiado from the Baixa-Chiado Metro Station. You are not taking the metro, only going to that station in Baixa, not too far from the Justa elevator, walking through the metro to the escalators which will drop you near A Brasileira. One note, I was there more recently in September and the escalators worked fine going up to Chiado, but broken going down. There are a few steps at the top when you get to Chiado.

I have not found a short-cut to walk up and down in the Alfama, but someone else may know of one.

I am a senior with mobility issues who spent a few nights in Lisbon a couple of years back.

It is a beautiful city and you will be staying in the Baixa area which is the flattest area in Lisbon. This is where i stayed and why.

Hills can be a problem for me and so is waiting in long lines.

There are about four or five hoho buses, each with a different route. You have to buy a ticket for each route but you get four when you buy three. I did not do them but you might like to look into the hoho buses and the different routes. However you might have long lines getting back on the bus after getting off.

Taxis are very reasonable in Lisbon. And so is Uber.

There is very good public transportation including. a trolley system which goes up and down the hills.

Your hotel or other lodging will probably help you with information and maybe even arranging excursions.

Some streets are pedestrian only and you will have to then walk. I walked from Rossio Square down to the water many times. It was a great walk.

There are also many places to sit down when need be.

In October, 2019, after a wonderful experience with Rick Steves' "Basque Country of Spain and France", we flew from Bilbao to Lisbon, rented an apartment for a week (near Rossio Square) and had a wonderful time. I am now 6 years older, and most of our Lisbon adventures would be nearly inpossible for me - physical limitations come with age - a cruel reality. Like you, I now walk with a cane, avoid stairs and find navagation around unfamiliar locations difficult.
Several suggestions listed in reply to your question seem good to me, but with one consideration. People with mobility issues often have difficulty with entering and exiting vehicles (cars, buses, trains, etc.) and, as you mention, stairs are challenging at best.
We hired Pedro from Cristina Duarte's "Lisbon and Beyond" for a walking tour. Pedro was excellent, and it is my guess he could easily provide a tour taking into account mobility issues. Cristina might also be available, but she leads Rick's Portugal tours so she is often unavailable. https://www.lisbonbeyond.pt/