To get the maximum support from the spider, bend the legs to fit the shape of the lamp. Then clean the spider assembly well with steel wool, or if particularly dirty with fine sandpaper, until it is bright again.
Apply flux and run a film of solder onto the legs where they will be in contact with the lamp. This will give you an indication of the amount of heat required to solder the legs to the lamp. It will also make it easier to fix the legs to the lamp once the appropriate temperature has been achieved in the legs.
You need to use the full power of your soldering iron, as the brass soaks up a lot of heat. If your iron is small you may need to change to one with higher wattage for this work.
As the heat is transferred quickly to all parts of the spider, wear gloves or hold with pliers while soldering.