Hi, MacMac,
There are lots of posts with information on the Caminho from Lisbon, and you will see there is a lot of debate. I walked it in 2008, so my info is way out of date, but even at that time, when there was more asphalt, no pilgrims, and no albergues, I enjoyed it very much. The forum resources section has a short guide to Lisbon to Porto, maybe now getting out of date and unnecessary because of all the improvements, but it may help you a bit.
https://www.caminodesantiago.me/community/resources/camino-portugués-lisbon-porto-2017.517/
One of the most notable changes in the route from Lisbon is that there is now an albergue in Alpriate, which is about 20 km from the Lisbon cathedral, where the arrows start. I think it has really made a difference in the experience. It's a small town with a great little café that serves reasonably priced meals, and the albergue brings together all those people you will be seeing over and over on the caminho. It's a good way to start off.
As far as walking out of Lisbon, I say go for it. The route from the cathedral to the Parque Nacoes takes you through the Alfama (old moorish quarter), the old port with some gorgeous buildings, past the tile museum (really worth a visit), and finally to the Parque Nacoes on the Tejo River. It was the site of a world expo and is also a fun place to visit (great aquarium, for example), but even if you are just walking through it's a nice river walk. There are some not so pleasant kms along a canal of the river for a few kms, but Alpriate is there waiting at the end!
There is probably as much asphalt on the Portugues as there is on the Norte, so shoes with more cushioning are probably a good idea rather than harder boots. And for an up to date list of albergues and other accommodation, check the list on the Via Lusitana website:
http://www.vialusitana.org/caminho-portugues/albergues/
There was a forum resource with a good compilation, but I can't find it, so if anyone else has the link, that would be helpful.
There is also a now outdated, but maybe still helpful, bit of suggestions of how to make the early stages shorter:
https://www.caminodesantiago.me/community/resources/short-stages-from-lisbon-to-porto.133/
Bom caminho to you and your daughter, Laurie