Lumberjacks appear in a broken bridge event. There are two versions of this event, one which includes fighting three undead lumberjacks and one that does not involve fighting (requires the player to instead cut trees to repair the bridge).
The best way to get the event is to use your escort's ability to scout ahead and check every path before choosing one. After their third level tier, the escorts can tell you what lies ahead, making it far easier to find the path containing the lumberjack event (the exceptions are with Rolayne Twickit, who can do so at only the first tier and Dean Vellio, who can do so at the fourth tier). Check each path before choosing one for the bridge event. If there is no bridge event, take the event which is easiest or fastest to complete or evade (however, time still vary to about 6 to 10 hours).
Another method is going to second phase using Rolayne and see if the event is ahead. when you encounter hop to another world after you killed 3 zombies. you can hop whenever you want and check if the event is ahead.
The Examine Text "He is one, but he's not alright" is a play on the refrain ("He's a lumberjack and he's ok!") from one of Monty Python's best known songs "The Lumberjack Song".
Previously, in a single event, the player would encounter 5 lumberjacks at a time (in waves of 2-3 and waiting caused more to appear), but after the update of the Temple Trekking activity, on the 17th of August 2011, only three lumberjacks will appear in a single event, and you are no longer guaranteed to get a lumberjack clothing item drop. However, the fact that you could potentially see the route ahead and that parts dropped on a cycle helped balance that out.
After the Evolution of combat, despite their high combat level, they have extremely low health, and seems to only be capable of hitting 1 (Monster Examine does not display a max hit at all).