Hi Chunlee,
The gain is S21 or S12, it is depend on which terminal is input (it is not a problem, am I right?
) . For the power gain, as we know, power=sqr(voltage)/impedance. So you can refer to this to calculate the power gain for different output impedance. During simulation, if your simulator can let you select the matching impedance at the output (e.g. ADS), that will be easy for you. If not, you need to calculate it by yourself. (According to the equation mentioned above). Let's assume, at the input there are , Vin, Rin and Pin, the out are Vout, Rout and Pout. So the power gain is Pout/Pin=(Vout/Vin)^2*(Rin/Rout). Normally the Rin=Rout=50, so the power gain is same as voltage gain, if Rin≠Rout, you need to care about the impedance ratio.
In s-parameter, the 50 Ohm is a widely used normalized value for simulation, you can specify different value, once you do this, you should keep in mind that your simulation is not refer to 50 Ohm. you may need handy calculate some results. If your simulator is good enough, it may convert it for you automatically, you can refer to the manual of your simulator to have an idea.
For the load impedance, it depend on the what circuit followed your LNA. Is it a filter or mixer or buffer. e.g. if the circuit is a mixer, you may specify hundreds Ohm or 1K for the load. I think you can just specify a value to have a try. Thank you.