I was on SummitClimb roster in 2010 for Everest North Col climb. Lhakpa Ri was specified as an alternative to NorthCol. After a small avalanche on the North Col wall one of the clients decided that he would go for Lhapka Ri instead. However that would require a dedicated sherpa/guide to go there with him and the company decided it against it so he simply turned out. I think he got some of his money back.
So I would double check with the outfit that they would take you there. The prices for SummitClimb were more reasonable, but it's a no thrills kind of a deal..