Neither full-back Hook nor flanker Lydiate has played since going off injured during Wales' punishing Pool D victory over Samoa 10 days ago.
Hook hurt his shoulder and was forced off at half-time, while Lydiate lasted just 11 minutes before an ankle ligament injury prompted an early exit.
Neither player will be available for Sunday's group finale against Fiji at Waikato Stadium, when Wales should comfortably book their last-eight place.
But the likely Ireland clash on October 8 is a target for both men as Wales continue building towards what they hope can be their most successful World Cup campaign since finishing third in 1987.
"Dan is now back running again after suffering an ankle ligament strain in the Samoa game," the Welsh Rugby Union's national medical performance manager Prav Mathema said.
Lydiate - part of an outstanding Wales back-row alongside skipper Sam Warburton and number eight Toby Faletau - has embarked on a heavy recovery process, which included getting up for treatment every two hours during the night.
Mathema added: "Dan has been incredibly diligent with his rehabilitation and his self-management.
"As a consequence, he has given himself every opportunity to be available for selection within the next two weeks.
"He still has a number of stages to complete within his rehabilitation, but we are confident that he will continue to make a swift recovery."
Like Lydiate, Hook missed Wales' record 81-7 World Cup win against Namibia in New Plymouth two days ago, but he is progressing at a similar rate to the Newport Gwent Dragons blindside.
"James has also been extremely thorough with his rehabilitation and is recovering well from the A/C joint injury to his shoulder," Mathema said.
"We are hoping to integrate him into full training towards the start of next week."
Wing Shane Williams, meanwhile, could be in contention to face Fiji after suffering from a thigh muscle strain that sidelined him from the Namibia encounter.
"Shane is recovering well," Mathema added.
"He is back up and running and we are pleased with his progress, but the next 48 hours will be essential in determining whether he may be available to us this weekend."
Wales coach Warren Gatland will name his team to tackle Fiji on Friday, with no fresh injury concerns reported following a 12-try romp at Stadium Taranaki
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