I don't have a lathe myself, but that would be the best way assuming it was good one that was well centred of course. I just used the mill, but a good pillar drill would work just as well for this. What I did was found a drill bit, (in this case 10mm), that fits pretty snugly into the current hole in the barb. You then put the barb in the vice and position it above the chuck that has the snug fitting drill bit in it. The barb should only be loosely mounted atm so you can get it to line up with the drill bit. It will take a bit of messing to get it in the right place. Once it will pass through the barb easily it will "self centre" the barb in the loose vice to the same plane as the drill bit, (the drill should not be running & don't force anything when doing this). When you have it pretty well centred the vice can be tightened, and double checked for position. I then just swapped to a 13mm bit without moving anything and ran through the barb. It gives a good true hole with only very slight run out.
If the pillar drill you are using is not to good, or you don't have a cutting lubrication /cooling fluid system you may find it better to go up in smaller stages, (10mm > 11mm > 12mm >13mm for instance.)
*Edit* the above assumes that the original hole is central, some of the 1/2" ones I have here atm are far from it
