What factors had caused Lobsang Jangbu to push himself to exhaustion both below and above camp four?

Factors that caused Lobsang Jangbu's exhaustion were as follows; his request to climb without supplemental oxygen, and his insistance on short roping, which is a technique used to help climbers, who were inexperienced, climb to higher altitudes.

One of the first people I passed when I started moving again was Scott Fischer's sirdar, Lobsang Jangbu, kneeling in the snow over a pile of vomit. Both Lobsang and Boukreev had asked for and been granted permission by Fischer to climb without supplemental oxygen, a highly questionable decision that significantly affected the performance of both men, but especially Lobsang. His feeble state, moreover, had been compounded by his insistence on "short-roping" the celebrity amateur, Sandy Pittman, on summit day.

“Short roping” is a technique designed to help inexperienced climbers reach altitudes higher than they could achieve by their own efforts.