"lack of ability to" is correct and usable in written English.
You can use it to express an inability to do something. For example: "She had a lack of ability to understand the math problem."
Too many tasks, lack of ability to prioritize.
This, we were told, can desensitise officers, leading to fatigue, lack of ability to cope and, significantly, lack of ability to empathise".
"But I question that lack of interpersonal relationship, and [current] lack of ability to accredit".
And probably shows a lack of ability to do something else.
"There is a lack of ability to evaluate the effect, to monitor it and a lack of ability to manage emergencies should they arise, and most people just do not have the experience in dealing with complications".
Is it a lack of ability to read defenses and study playbooks on the part of African-Americans?
"It's another example of Wal-Mart's lack of ability to track the specifics of its supply chain," she said.
"There can be a lack of ability to communicate whatever expertise they may or may not have," Ms. Meltz said.
The tranquilized market reaction reflected a seeming lack of ability to feel much anger or sadness during the battle.
The choreographer and my on-ice partner were so patient with my complete lack of ability to memorize choreography.
