The Botany Lab seems to be a place where the original owner of the Haunted Towers would do experiments and such. The room is divided into a lower half and a slightly higher-in-altitude upper half which Luigi can only cross via a two-step staircase on the right-hand side of the room. On the center of the upper half of the Botany Lab, there are three tables that have test tubes and various other containers that are holding different-colored chemicals. There is also a bucket on one of the tables. On the right side of the upper half, there is one flower that Luigi can flash his Strobulb at for a few dollar bills. Next to it seems to be a growing sprout. On the left-hand side of the upper half of the room, you can collect a few coins.
Moving down to the lower half of the Botany Lab, on the left, there is a hydro generator that needs to be activated by flashing your Strobulb at three separate switches simultaneously, to make a water source from the ceiling start up. This allows you to fill the bucket with water and water the flower in the upper-right corner of the room, and get a gem from it. If you restore the missing part of the pipe with your Dark-Light Device, you can activate the hydro generator again, causing the plant in the center of the room to grow and break the container it was sealed by. From there you can proceed to the next floor, by climbing up the newly sprouted plant. There is a poster on the left wall on the lower half, which when sucked up will give you some money.
There are also vines, flowers, and pipes all over the place.
You only need to go the Botany Lab in the mission B-2 "The Pinwheel Gate", where it is only used as a way of progressing to the next floor.