This is classic Chinese negotiation tactics, I have been dealing with this on a business level for 20+ years:
The deal is hammered out with someone with apparent authority but they need to go to their boss/owner for "final" approval, they come back with major changes to hard fought deal points to buy time and save face and you have to walk away for a while until they are ready to finally agree. Patience is key for Western negotiators, the Chinese rightfully don't think we have it.
There are eight elements for Chinese negotiations:
Guanxi (Personal Connections)
Zhongjian Ren (The Intermediary)
Shehui Dengji (Social Status)
Renji Hexie (Interpersonal Harmony)
Zhengti Guannian (Holistic Thinking)
Mianzi ("Face" or Social Capital)
Chiku Nailao (Endurance, Relentlessness, or Eating Bitterness and Enduring Labor through Patience)
Vice Premier Liu, the Zhongjian Ren, handled everything for Premier Xi but it was Xi and the Politboro who ultimately have to approve the deal and thought they would lose Mianzi if they immediately agreed to the deal, so negotiations entered into the predictable Chiku Nailao phase.
I think that Lighthizer realizes that showing US patience is a sign of chiku nailao. The Chinese rarely make large concessions following persuasive talks without broader consultation with the leaders and thorough group decision making and social status (shehui dengji). Moreover, the Chinese are skilled in using delay as a persuasive tactic, so Lighthizer has realized that he has had to bide his time. This allows the Chinese to use the lulls in the negotiation cycle to consider any new information, develop more questions and ultimately save Mianzi.
In the end, the investment in time pays off once the Chinese have completed their negotiation cycle.