[midnightpulp]

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I consider my postflop playing skills to be quite well but it is impossible to gain any information from Mr. X by betting and raising.

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Don't worry as much about gaining information as extracting the maximum from LAPs.

These players are just about impossible to read. Like you said, they play a draw, bottom pair, middle pair, top pair the exact same way: call, call, call.

However, these are traditionally the easiest opponents to crush. Sounds like you're experiencing a bit of variance where they seem to always "have it."

I can assure you, this will change, and you'll be smiling as they call your turn raise and river bet with bottom pair.

Do not avoid these opponents, seek them out and engrave their screen name into your buddy list.

Also, try to determine the breed of LAP you're against. Is he the type to only bet top pair on the end when you check to him? If so, you can safely fold your weaker hands. Is he capable of the occasional bluff? Of value betting weaker holdings such as middle pair or top pair no kicker?
What type of hands he does raise? Etc, etc...

When you managed to figure out his habits, make the proper adjustments.