"out of a lack of" is a correct and usable phrase in written English.
It is typically used to express the reason or cause for something being done or not being done, often indicating a sense of deficiency or scarcity. Example: Out of a lack of resources, the company had to downsize their staff.
"It is born out of a lack of opportunities.
"Businesses do not do this sort of thing out of a lack of self-interest, but perhaps out of philanthropic self-interest," a mining company executive said.
A feeling of inferiority – born out of a lack of love from his mother – pervaded his appreciation of his own talents.
"They have cornered themselves out of a lack of influence on any of the parties that are driving this -- Hezbollah, Hamas, Syria and Iran.
Ed Miliband failed to do that, so I voted Conservative again this year - more out of a lack of choice than a resounding desire.
It doesn't have villains, because I don't think that Germany is doing it with bad intentions but it's happening out of a lack of understanding of very complex problems.
He told Panorama that consumers were losing out because of a lack of competition in a marketplace dominated by a small number of big banks.
A source said it believed that "too often in the past, university applicants have missed out because of a lack of opportunity to demonstrate their potential".
But the law has not been carried out because of a lack of money to provide the required housing, care and treatment.
And big six should really read big seven, because the National Grid, too, is stuck in the past and frightened of the future, just as the lights are in danger of going out because of a lack of new investment.
But to have two or three thrown out because of a lack of evidence, that doesn't tell me there's a problem".
