Have a look in Ardy's for lighting, Just down from Carrefour. You can see the Ardy's sign high above the houses and to get to it you need to turn just after the Carrefour roundabout as though you were going into McDonalds. Follow the slip road and take the right hand fork, the entrance to Ardy's is further down on the left.
Cheapest place I've found for lighting in the area, I've bought a mother and baby standard lamps in there for 16e (one large lamp and a smaller reading lamp which can be adjusted).
If you have the time look in the second hand shops, there are quite a few around. Not sure where you are based but there's one by the Park of Nations called Rincon Crisis which may have what you're looking for. Can't find the exact address but if you park near the park and walk along you should find it.
In Torrevieja Ramon Galud, there are 3 todo shops close to the Church square where you can pick up bargains for the house.
I'd also join the forums dedicated to Torrevieja as they have sections for items for sale, you might find patio furniture there. If you're not in a hurry you can kit the house out with the basics and buy the rest later.