The Clayman Lab is the area in Mother 3 where you go to work part-time so that you can get into Club Titiboo and find Lucky/Duster. Anybody who works here will be given a free pass so that you can go to the Club that night.
This place is up north of the Train Station east of Tazmily Village. This is the only way to get there, as the train is not running to and from the station unless you work there, which it doesn't even start running when you are a part-timer.
Here is where you work part-time as Lucas so you can go get Duster. This is a spot that Claymen are found working, and sometimes snoozing on the job. Those that are tired must be taken back to one of the first rooms. You have to do this three times to get through with this area. After completing it, you will be paid with a few items, and then rewarded with the Club Titiboo Ticket. You can always come back for more things, but you cannot obtain the Ticket anymore, as yours will work anytime throughout the game, as people abandon the Club.
This spot only appears in Mother 3. On the outside it looks like an old building, and on the inside it looks like a beautiful building. Once you go downstairs, all of this changes. You will find that this place looks like a Mine, but really torn up and destroyed. This is the area that all of the Claymen work. It is basically a lot of ground with a few indents in the ground for you to go farther down. Of course, like a mine, this area also has little doors for you to go through. You will find that it is impossible to go very far in the mine though. At the very beginning of the mine, there is a little elevator for the Claymen. A Pigmask operates this, so you can get the Clayman back up to the next floor without pushing him up the Rope Ladder.