Most of the time ship lap is done horizontal on ballon framed buildings and it's a good application as the rabbet acts as a drip edge. Just to be clear as some people refer to board and batten siding as ship lap (which its not) and it is vertical on post and beam framing but ship lap could be to, not common here. Both of these are for open walled structures not sheathed and insulated ones.
You didn't mention if you are insulating, what type of sheathing, or heating but I am assuming it going to be heated and is sheathed in OSB. What you want to do should not really be done. No siding is water proof. Wind blown water, dew, and capillary action allow water behind the siding. Capillary action on vertical ship lap would be worse than it applied horizontal but on a timber framed barn with open walls it will dry out very quickly. If wood siding(really all siding) is place over sheathing it needs to have a rain screen. This is tar paper applied horizontally lapped top over bottom. Then vertical furing strips are screwed to where the studs are. A strip of tar paper covers the the furing strip and the siding is applied horizontally,nailed through the furing strip into the stud then thin long siding nails. This air channel allow natural convection (heat rises) currents to dry the wood evenly and any droplet moisture to run out the bottom. If one primes the back as well as paint the front moisture expansion/contraction in the wood is mitigated and the paint doesn't crack and peel nor does the OSB rot or the insulation become saturated. Also cupping is mitigated. To all the nay Sayers at this point look up tyvek failure and read some articles on fine home building or JLC.
So if your still with me we will move on to vertical intstall. If we just fir out the wall horizontally there is no natural convection as the siding is heated by the sun(hot air/water vapor goes up not sideways) and any dropplet water hits the strip and forces against either the sheathing or siding causing rot. This would still be better than attaching it directly to the sheathing as there would be some air movement sideways but not even or consistant.
I SUPOSE one could take and put two layers of furring strips, one vertical against the sheathing 1/2 thick and then a thicker piece screw through the strips and sheathing into studs for the siding to be attached to but then it starts getting shady structurally.
Wish you the best of luck. Also if you do end up doing it remember to put the outside edge of the rabbet down wind of your typical prevailing winds to lessen the water egress. Good luck. For longevity of the structure and your pocket book I wish you would consider putting it on horizontal. If it were an unsheathed/Unheated barn I would say have at it but I don't think it will end well