Lelouch only admitted his inferiority to Schneizel before, not at present. He currently believes that he is either on par or above Schneizel's intellect, as shown by his comment during the chess match. I agree with his belief (they did tie in the chess match, whereas before I bet he lost miserably enough to admit it), though I have to admit he is still not up to Schneizel's cruelty and ability to control his emotions.
About the quicksand loss Lelouch suffered... It was practically impossible for him to know that the money supposed to be put into that land disappeared due to corruption, since there is probably no record of it (well, it is illegal, no matter how common) anywhere. Even with enough time, I doubt he could have gained such information, especially since he probably thinks that the info he got on the battleground was sufficient.