Sentence examples for for a lack from inspiring English sources

The phrase "for a lack" is correct and can be used in written English.
It is typically used to express a reason or cause for something that is missing or deficient. Example: "The project failed for a lack of proper planning and organization." This means that the project was unsuccessful because there was not enough planning and organization put into it. Another example: "I couldn't finish my dinner for a lack of appetite." This means that the speaker was unable to finish their meal because they did not have enough of an appetite.