matching an LNA

i have a thought in my mind and if i am wrong i need someone to correct it for me..
i know that matching assures that there no reflections back to the source while conjugate matching assures the max. power transfere which we need in LNA to obtain max. gain. but conjugate matching yields reflections back to the source...so what i noticed in Pozar and Gonzales books that we first make a matching to the 50 ohm line and then make a conjugate matching to the input to the LNA to assure max. power transfere and no reflections back to the source at the same time...is that a true guessing or i am just wrong.

No, you think in wrong as I understood because you question is not very clear.
When you depart from input impedance of a system to arrive 50 ohm and the circuit that you obtained will show always conjugate impedance of lna.
Conjugate matching means that to find circuit so that it will meet the transfer function with a impedance desired.

I think it's clear...

Assuming that the matching network is a 2-port network, and it is composed of pure lossless L and C, port 1 matched means that port 2 is also matched. So if port 1 is matched to 50 ohm, that means port 2 is matched to Γin*, automatically.

You can think in this way: If the matching network is composed of lossless LC, then it will not attenuate the signal power in both direction, namely the matching network is lossless. If LNA input interface is mismatched, a portion of input signal toward LNA is bounced back to port 2 of matching network. Since the matching network is lossless, it just pass the bounced singal through port 1 to 50ohm antenna. So, port 1 is IMPOSSIBLE to be matched because the bounced back signal always exists, and we know a matched port means no reflected power. On the other hand if port 1 is matched, that means no reflected power at 50ohm interface, and this means that there is no reflected power at the input interface of LNA because matching network is lossless. Therefore port 2 is also matched.

But if the matching network contains RESISTOR, namely it is lossy, then the above is not true. For example, you shunt a 50ohm resistor directly to the input of LNA for 50ohm match, you'll get a matched 50ohm seeing from 50ohm antenna(mathced :) ), and a 25ohm seeing from LNA interface(mismatched :( ).