not lack anything何一つ means “not even one thing,” and 不自由 means “inconvenience” or “lack of something needed.” This phrase is commonly used with はない, しない, or させない to mean that someone has everything they need and is not inconvenienced in any way.
JA: この家では何一つ不自由なく暮らせます。
EN: You can live comfortably in this house without lacking anything.