Did you drill drainage holes in the barrel? If not, then your barrel may not be draining and is soggy, soaking wet at the bottom.
I made this mistake many years ago. The wood in those barrels are designed to swell and keep liquids in.
If you didn't drill holes, you can drill them now all around the sides at the bottom, (above the base), without disturbing the lemon.

wanda

You did not say how large a pot your tree was in before you transplanted it. If it was in a 3 gallon or smaller pot a step up to a half barrel is a big move. Unless your potting soil was based on ground bark with a generous amount of sand(which is what the commercial growers use)you can expect the soil to remain too wet even if you water only twice a month. I would do as Wanda has suggested in any case, as you can't have too much drainage. Al

If you haven't already, you might want to invest in a moisture meter. Mine was about $7.00, and I was surprised at the difference in moisture at the top versus the bottom of my containers. I was trying to figure out a good watering schedule for my potted citrus. I ended up with what Calistoga and Wanda mentioned...soil with a good amount of bark mixed in, lots of drain holes, and I potted up from 5 to 12 gallon containers.
If moisture doesn't seem to be the problem, you may want to try an application of iron chelate. I used it once on citrus tree and the yellowing cleared up quickly.

Take some of the yellowed leaves to a Certified Nurseryman at a good nursery. They can tell you what the problem is.