Can this work straight on studs-no sheetrock?

Personally... I would do without the sheetrock / drywall - but you might want insulation behind the shiplap (which is basically just wooden slats installed horizontally) - so go for it!

You can put up a ship lap type of wall... it is what was used before dry wall... just make sure you insulate behind it... bead board would look good too.

Also I have seen some of the DIY TV guys use a composite/concrete siding like material, and install it to look like ship lap (they used it in a kitchen around a stove, fire issues) If you have moisture or possible flood issues in your basement... composite would be the way to go.

How cold or warm is your basement? If insulation has been added you could be good to go, BUT, consult your local building codes. Think of your future heating and cooling costs for the space and let that be your guide.

It depends of if you're going to use real shiplap or faux shiplap. It's my understanding that shiplap has a rabbit connection but faux shiplap is created from regular boards using something like a nickel to space the boards apart. If you do that there will be a space between each of the boards that will show what's behind the faux shiplap. Not only that, but it will cause cold air to come into the basement. I'm thinking that there may be something else that's less expensive that you could use behind it. You could ask at Lowes, Home Depot, Menards or wherever you plan to buy your boards. Also check on Craig's List to see if anyone is selling left over materials that would work for you. Here's another person who asked the same question. You can read other answers there as well. Wishing you the best.

No sheetrock Just shiplap it

Use PINE shiplap boards..They come 6 or 8 " wide DONOT use the manufactured stuff

You DO need the sheetrock. Not only is it CODE, its a moisture barrier, but also a fire retardant. Depending on the thickness it can withstand direct flame from 30 minutes up to one hour. With only shiplap that fire retardancy is 0. Meaning flames would just shoot up the wall cavities into the rest of the living quarters.