I visit Hong Kong several times a year, and never count on the LCDH... I have never had a great cigar from there...
I usually stay at the Peninsula hotel in HK. They have the Davidoff Shop in their lobby. It is very small, but hardly ever has anyone in there... I usually bring my own cigars in, even though there is a sign saying that is not allowed... a little tip goes a long ways... As soon as you walk in, their humidor is on the right. They have some Regionals and LE's, but are bland and not very good. They do not sell boxes of Cubans... The next place I frequent is the LCDH at the Sheridan in Kowloon. This place is twice the size of the Davidoff shop, but again has very little to offer. You can buy a cheap cigar as you walk in, then go to the back lounge and light the one you brought with you... Make sure you tell the cute hostess that you will light it yourself, or they will follow you back, sit you down and proceed to light your cigar for you, taking their time, and waving it rapidly in the air, until you have a perfect light... They do sell boxes, but are expensive. Another lounge is in the Mandarin Oriental, called Cuban Cigar Divan. It is a small lounge very similar to the Davidoff Shop...
My favorite place to is the Red Chamber Cigar Divan, located in the Peddler building in Central. This place is beautiful. They have hundreds of selections, and carry aged, regular, LE's and RE's... They even have Dunhills and Cuban Davidoffs, but expect to pay upwards of $4000 HK for a single (about $500 US) If you tip Mr. Wan (the manager) when you walk in, they will put you in the VIP area, and treat you like a king... This is where I keep my cigar locker, so i don't have to carry my cigars in and out of the country all of the time... They are also the only cigar lounge with a full bar, and a menu to order food. They have free WiFi, and several TV's... I spend a lot of time at this place...