"acute lack" is correct and usable in written English.
You can use it when you want to emphasize a deficiency of something e.g. "The company was suffering from an acute lack of resources."
"It's true," says a humanitarian worker, "but there is an acute lack of planning and supervision".
Due to an acute lack of bicep, my armband has long since slipped off my arm and been lost.
Acute lack of credit is also Felix Magath's problem at Schalke, albeit in a more literal sense.
Such a commitment could have a profound effect on the fight against AIDS by overcoming an acute lack of resources in the poorest and hardest-hit countries.
Though obviously not comparable to a strip club, planting a large new mosque directly on that site would nonetheless show an acute lack of sensitivity.
Clapson, 59, who had diabetes, died in his flat in Stevenage on 20 July 2013, from diabetic ketoacidosis (caused by an acute lack of insulin).
Obstinate, they try to make the facts fit the ideology: there is no shortage of people for jobs, just an acute lack of jobs.
Number 23's predicament last week saw it thrust to the centre of protest over the acute lack of London's social housing.
Not selling the property would create an acute financial lack that would significantly impact your life.
The staff in the ED at the Moi Teaching and Referral Hospital continue to face the health care challenges of HIV on a daily basis: the difficulties of diagnosis and testing in the acute setting, lack of knowledge, and fear of open discussion due to stigma.
Most current treatments for acute cough lack evidence-based proof of efficacy to support their use.
