I have no experience with donkeys, but lots of experience with hoof problems in horses.
For horses, it's very rare for laminitis to occur in one foot - it's usually in both fronts or all four. The usual cause of laminitis in one hoof only is a severe problem with a non-weight bearing hoof beside it. For example, if a horse had surgery on his left rear, then his right rear would be at risk for laminitis because it's holding up his weight all the time, and he may even be hopping on it which would be even worse. (This is what killed Barbaro). So it's extremely unlikely your horse has an active case of laminitis.
Founder would be even rarer - that's when laminitis is so bad the bones in the hoof change position. The new, rotated position of the bones is permanent, and contributes to further hoof pain.
However, your donkey could have foundered in the past. This often contributes to white line disease and even a tendency to abscess in affected hooves.
Repeat abscesses are not rare, unfortunately. They can result from an abscess not fully draining the first time, or an abscess with multiple tracts and/or pockets where all did not resolve, or an abscess treated with antibiotics that seemed to heal but was still brewing, and so on. They can also result from underlying metabolic issues (such as Cushings) which suppress the immune system.
It can also be a more serious issue. I've had two horses where the abscess had infected the coffin bone (requiring surgery), and one horse with an infected pastern joint (untreatable, euthanized). In all three cases, vets originally diagnosed abscesses (which I treated scrupulously) but the abscess either recurred or masked another condition. The joint infection horse had a suppressed immune system due to Cushings.
The infected coffin bone horses were diagnosed with xrays; the infected joint horse through a joint tap.
To me, in your case, the softness in the coronet band, combined with his history, makes me think an abscess is very likely, and that it's going to erupt in that spot. It would be advisable for the vet to come out and do an xray, which would reveal the state of the coffin bone and also reveal if the donkey had foundered in the past. In the meantime, until the vet gets out, I would soak the foot in warm water with epsom salts several times a day, then poultice and pack it, to try to get it to erupt more quickly.
So, long story short, yes, call the vet! :)