[Freakaloin]

Could I attach drywall directly to this 1" thick lap and gap siding or should use furring strips or something?

http://imageshack.us/a/img19/699/imagejlf.jpg

 

[ToolSeeker]

I would say yes go right over it.

 

[joecaption]

Are you getting rid of that sliding door? Not sure how your going to attach casing to it.
If you used 1/4 you would not have such a big problum trimming out the door, and you could kill the power to the outlet then remove the screws holding the in place and twist it from to to bottom to get it out of the way, install the sheet rock then reinstall the outlet without having to use spacers.

When trimming out the door I would assemble it laying down and use Tite Bond II and nails in both directions then you leave the sheetrock back far enough that the casing will have room to flex and fit flush.

 

[spaceman spif]

If it's 1" thick, you should be able to attach to it without furring strips as long as it's a relatively flat surface. But I have to admit, I think that siding actually looks kinda neat. You sure you want to cover it?