I'm not sure why you are posting this in the Lagos forum given your itinerary. Lagos is very small compared to the other cities you mentioned. We have none of the big names you mentioned here. In the Algarve you would be restricted primarily to the Algarve Shopping Centre near Guia/Albufeira. There is a Zara there, as well as a Bershka if I remember correctly.
Zara is actually Spanish owned and as VAT is lower in Spain than in Portugal, prices may be lower. However, be aware that design styles are for Spanish Tastes.
There are at least two Zara stores in downtown Seville.
In Lisbon, you should head to Centro Commercial Colombo - Metro Stop Colegio Militar / Luz. All the big names are there.
I'm not sure though if prices will be competitive in terms of the "Looney"
