An Undead Lumberjack is a monster that can only be fought during Temple Trekking / Burgh de Rott Ramble. They come in nine different levels, as seen in the table below. In each event where the lumberjacks attack, the player can get one piece of lumberjack clothing (you can receive only one piece of clothing per event).
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.
The Examine Text "He is one, but he's not alright" is a play on 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.
Before an update the lumberjack top was a much rarer drop than the other parts. When asked about this Jagex assured that there was an equal drop chance for all parts. However players would often have 5 or more of every other piece before getting a top. Eventually Jagex realized that the lumberjack pieces had an equal drop chance per bonus experience they provided. Since the top provided a greater amount of bonus experience, it was much less likely to be dropped. Jagex has fixed this now.