Lhakpa Ri is in Tibet and accessed from the ABC of Everest north side BC.
It would be an expensive trip for an operator to run just on its own, so check out whoever runs Everest north side trips - SummitClimb, Adventure Junkies, Adventure Peaks (UK) etc. as well as Asian-Trekking and Monterosa Nepal for cheaper options.
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..