I am traveling to either Lisbon or Barcelona in January with my 60 yr old mom who is active-not sure which city wouold be better and have better weather as well-any suggestions? we like to tour, shop, sit in cafes etc

If we talk about weather, then the answer is Lisbon It's very much southern so weather is not so cold. Anyway, they still will be in January.
Both are wonderful cities where there's a lot to see and do even in January

I spent my birthday in Barcelona last Jan. I thought the weather was quite pleasant with days in the mid sixties and plenty of sunshine. I wore jeans, mid-weight tops,a sweater and was comfortable in sandals. However, the locals were bundled up in dead of winter boots,scarves and wool coats.
You will find lots to do and see in this wonderful city. We used the DK Eyewitness Top 10 Barcelona book as our guide. The food was great, people were friendly and the city was easy to navigate.
My only complaint was I didn't have a direct flight so we wasted precious time in Madrid making a connection. I have decided that if my trip time is less than a week I'm flying direct from now on. So, if that is a factor for you, I'd choose whichever city gives you more time because I imagine you would enjoy both.

If I was given the choice, I'd pick up Barcelona

I think the weather should be better in Barcelona. I've twice been there in March and both times it was warm & sunny (t shirt weather) during the daytime, in the sun, although I needed a jacket at night. My PILs went to Lisbon in March and it was very cold, rainy and windy - I gather the wind is a common feature. Although it's a bit further south (not much), Lisbon is on the Atlantic where the prevailing winds come from, whereas Barcelona is on the Med.