Lasing in a 2-Level system? What exactly is the difference between 2-Level, 3-Level and 4-Level systems? Why can we not achieve stimulated emission in a two-level system using optical pumping?
 A: For beeing texbook knowledge about the four laser demands population inversion, laser threshold, energy source and active medium I'll answer the question in a concise way. In your active medium of the unpowered laser is thermal equilibirum. It's governed by Boltzmann law. So higher energy levels are less populated.
Turning the power source on populates a high energy level. The population inversion is maintained by optical pumping to a third level. There is a quick radiationless process to "fill the higher level". Quick compared to radiation process. Key point: 3rd level for maintaining population inversion.
Population inversion of two levels: The lower level is less populated contradicting Boltzmann law. Lasing process takes place in these two levels. This process is stimulated emission. The incoming photon "has been cloned" ;) wavelength, polarisation und direction of the second new photon are identical. Energy for creation of this photon is taken from the system. System ends up in the lower level state. 
A: Strictly speaking, you don't need population inversion for lasing. LWI (lasing without inversion) exploits quantum interference (closely related to Electromagnetically induced transparency).
Observation of lasing without inversion in a hot rubidium vapor under electromagnetically-induced transparency conditions
A: Optical pumping will at most only achieve equal population of a two-level system. This is because the probabilities for raising an electron to the upper level and inducing the decay of an electron to the lower level (simulated emission) are exactly the same! In other words, when both levels are equally populated, the numbers of electrons "going up" and "down" will be the same, so you cannot achieve population inversion which is required for lasers.
The solution is to use a third metastable level. The pumping will be between the other two, but electrons in the upper energy level will quickly decay into the metastable level, leaving the upper level practically unpopulated at all times. The transition from the metastable level to the ground level has a different frequency: the laser frequency. The  pumping frequency is between upper level and the ground level, so the pumping is off-resonant to the laser transition and will, thus, not trigger stimulated emission.
