How to convert this outdoor lamp box to GFCI receptacle?
Surface mount a weatherproof 4/O box extension over the top of your existing box and feed the wires through the back. Seal around the box where it meets the wall so water cannot get behind it.

Then install a weatherproof conversion cover, they are fairly new and I have only seen them on the internet. Then install a weatherproof receptacle cover and you are done!