His acceptance of Lu Xun's letter is quite likely from arrogance, considering that was the point of the letter. Lu Xun lays out Guan Yu's condition quite well in a conversation with Lu Meng, "Guan Yu, proud of his own valour, is disdainful towards others. He has just accomplished something great, and now he has become overly arrogant, thinking only to strike northward. Since he hasn’t suspected much activity from our side, once he hears of your illness, his defences will certainly drop." *Lu Xun's SGZ
The simple fact is that his arrogance is well known within other kingdoms. Also the fact that Lu Xun would be willing to risk a large scale operation in great deal because of his arrogance is also telling. From the eyes of Lu Xun certainly his arrogance would be a facet of his downfall. He then makes moves to exploit this, quite successfully, with his letter. Besides a letter that flattering would probably cause some suspicion with anyone who doesn't think too much with their ego.
In addition to Guan Yu's many other noted moments of arrogance and Chen Shou's note it makes one wonder what did not make it into the chronicles.