I have heard many people saying that Lasker used psychology to win. But I have also read a Wikipedia page mentioning recent researches refuting this belief and justifying Lasker's tactics to be quite ahead of his time and something laden with a hidden master plan. I need to know if there exists any such analysis which is available online so that we can know the truth ?
We can't know the truth. Lasker is dead and he's the only one who knows if he really played like that intentionally. We can create an absolutely perfect analysis of his games and still never know if he intentionally played a bad move that happened to work out in a particular game or whether he just made a mistake and didn't get punished for it.
Good moves will beat psychology every time, but even so there exists ample evidence to support the idea that sometimes moves that are less than perfect will win games because they fit in with the psychological moment.
My own opinion? I think Reti invented that as an excuse to cover the fact Lasker was making moves he (Reti) couldn't fathom. Not that Lasker never played the man instead of the board, but that he didn't do it as often as Reti would like us to think he did.
I need to know if there exists any such analysis which are available online so that we can know the truth ?
I don't believe any such analysis exists online. The closest you will come is the excellent book by GM John Nunn confusingly called John Nunn's Chess Course
This is actually a book in which Nunn dissects in great detail a number of Lasker's games including a lot of high quality new analysis. Nunn looks particularly critically at previous analyses by other writers which suggest that Lasker made doubtful moves against some opponents which caused his opponents to go astray and lose the game when with best play they should have won from those positions.
Nunn shows that these analyses are wrong and that the so-called "bad" moves were actually very good moves not only in terms of computer analysis, in that they addressed the tactical and strategic needs of the position, but also in terms of making life difficult for the opponent by giving him lots of plausible possible continuations and therefore lots more chances to go wrong.
I know that there has been some analysis done which compares computer moves to historical games. Here is a wikipedia article including that comparison and also some other measurements for comparing players throughout history:
Perhaps the Lasker wikipedia page refers to one of these kind of measurements.