Decathlon is my go-to gear store anywhere in the world, and they have a shop in Lugo. It is quite out of the city centre though, so you may look in the list @mspath posted to check which ones are close to your accommodation.
I was in Lugo a few years ago during the national day so could only find a hotel in the outskirts (mainly occupied by police in town for duty) and found the local bus system pretty inexpensive and efficient, so that option is always open.
I wasn't looking for other items, but they seemed to have a decent selection of clothing. There's a pharmacy and a good supermarket within about 100m too, so a pilgrim is able to get most things they need in a small area.