I've tried to solo Lazy Laurence a couple of times as an arcanist (first time I was only ~27, the second I didn't have the summoner soul and my chocobo made a poor tank on its own); I held my own, but I couldn't outpace the timer, even though I never stopped casting for even a moment
The second time was far more successful as I had a chocobo to add to the damage, even getting Laurence down to 10% health before the time ran out. The extra wave of adds it summoned at low health really made juggling damage and healing a mess though, which is especially a problem when damage is how I got the MP to heal with.